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  • 1.
    Aaltonen, Harri
    et al.
    Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland.
    Sierla, Seppo
    Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland.
    Kyrki, Ville
    Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland.
    Pourakbari-Kasmaei, Mahdi
    Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland.
    Vyatkin, Valeriy
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Computer Science. Department of Electrical Engineering and Automation, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland.
    Bidding a Battery on Electricity Markets and Minimizing Battery Aging Costs: A Reinforcement Learning Approach2022In: Energies, E-ISSN 1996-1073, Vol. 15, no 14, article id 4960Article in journal (Refereed)
    Abstract [en]

    Battery storage is emerging as a key component of intelligent green electricitiy systems. The battery is monetized through market participation, which usually involves bidding. Bidding is a multi‐objective optimization problem, involving targets such as maximizing market compensation and minimizing penalties for failing to provide the service and costs for battery aging. In this article, battery participation is investigated on primary frequency reserve markets. Reinforcement learning is applied for the optimization. In previous research, only simplified formulations of battery aging have been used in the reinforcement learning formulation, so it is unclear how the optimizer would perform with a real battery. In this article, a physics‐based battery aging model is used to assess the aging. The contribution of this article is a methodology involving a realistic battery simulation to assess the performance of the trained RL agent with respect to battery aging in order to inform the selection of the weighting of the aging term in the RL reward formula. The RL agent performs day-ahead bidding on the Finnish Frequency Containment Reserves for Normal Operation market, with the objective of maximizing market compensation, minimizing market penalties and minimizing aging costs.

  • 2. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 15, p. 79-116Article in journal (Refereed)
  • 3. Abarbanel, Saul
    et al.
    Ditkowski, Adi
    Gustafsson, Bertil
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    On error bounds of finite difference approximations to partial differential equations: Temporal behavior and rate of convergence2000Report (Other academic)
    Abstract [en]

    This paper considers a family of spatially semi-discrete approximations, including boundary treatments, to hyperbolic and parabolic equations. We derive the dependence of the error-bounds on time as well as on mesh size.

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  • 4.
    Abbas, Qaisar
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

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  • 5.
    Abbas, Qaisar
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak Boundary and Interface Procedures for Wave and Flow Problems2011Doctoral thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems.

    The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case.

    The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach.

    Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks.

    Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability.

    Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

  • 6.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    A weak boundary procedure for high order finite difference approximations of hyperbolic problems2011Report (Other academic)
    Abstract [en]

    We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.

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  • 7.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
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  • 8.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 9.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak versus strong no-slip boundary conditions for the Navier-Stokes equations2010In: Engineering Applications of Computational Fluid Mechanics, ISSN 1994-2060, Vol. 4, p. 29-38Article in journal (Refereed)
  • 10.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Weak versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations2008In: Proc. 6th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2008, p. 52-62Conference paper (Other academic)
  • 11.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 12.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accurate and stable calculations involving shocks using a new hybrid scheme2009In: Proc. 19th AIAA CFD Conference, AIAA , 2009Conference paper (Refereed)
  • 13.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Faculty of Engineering Technology, University of Twente, AE Enschede, The Netherlands.
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy Stability of the MUSCL Scheme2010In: Proc. 7th South African Conference on Computational and Applied Mechanics, South African Association for Theoretical and Applied Mechanics , 2010, p. 65:1-8Conference paper (Other academic)
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  • 14.
    Abbas, Qaisar
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 15.
    Abbas, Qaisar
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    van der Weide, Edwin
    Nordström, Jan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Energy stability of the MUSCL scheme2010In: Numerical Mathematics and Advanced Applications: 2009, Berlin: Springer-Verlag , 2010, p. 61-68Conference paper (Refereed)
  • 16.
    Abdallah, Nancy
    et al.
    University of Borås, Faculty of Textiles, Engineering and Business.
    Schenck, Hal
    Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four2024In: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 121, p. 102257-102257, article id 102257Article in journal (Refereed)
    Abstract [en]

    In (Stanley, 1978), Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1,13,12,13,1). Migliore-Zanello show in (Migliore and Zanello, 2017) that for regularity r=4, Stanley's example has the smallest possible codimension c for an AG ring with non-unimodal H-vector.

    The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c=3 it is conjectured that all AG rings have WLP. For c=4, Gondim shows in (Gondim, 2017) that WLP always holds for r≤4 and gives a family where WLP fails for any r≥7, building on Ikeda's example (Ikeda, 1996) of failure for r=5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c=4 and r≤6.

  • 17.
    Abdul Salam, Parveena Shamim
    et al.
    Tu Kaiserslautern, Germany;Iit Madras, India.
    Bock, Wolfgang
    Tu Kaiserslautern, Germany.
    Klar, Axel
    Tu Kaiserslautern, Germany.
    Tiwari, Sudarshan
    Tu Kaiserslautern, Germany.
    Disease contagion models coupled to crowd motion and mesh-free simulation2021In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 31, no 6, p. 1277-1295Article in journal (Refereed)
    Abstract [en]

    Modeling and simulation of disease spreading in pedestrian crowds have recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics, we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts, the influence of contact times has also been modeled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated, including uni- and bi-directional flow in a passage with and without obstacles.

  • 18.
    Abdulla, Parosh Aziz
    et al.
    Uppsala Univ, Sweden.
    Atig, Mohamed Faouzi
    Uppsala Univ, Sweden.
    Chen, Yu-Fang
    Acad Sinica, Taiwan.
    Phi Diep, Bui
    Uppsala Univ, Sweden.
    Holik, Lukas
    Brno Univ Technol, Czech Republic.
    Rezine, Ahmed
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Rummer, Philipp
    Uppsala Univ, Sweden.
    TRAU : SMT solver for string constraints2018In: PROCEEDINGS OF THE 2018 18TH CONFERENCE ON FORMAL METHODS IN COMPUTER AIDED DESIGN (FMCAD), IEEE , 2018, p. 165-169Conference paper (Refereed)
    Abstract [en]

    We introduce TRAU, an SMT solver for an expressive constraint language, including word equations, length constraints, context-free membership queries, and transducer constraints. The satisfiability problem for such a class of constraints is in general undecidable. The key idea behind TRAU is a technique called flattening, which searches for satisfying assignments that follow simple patterns. TRAU implements a Counter-Example Guided Abstraction Refinement (CEGAR) framework which contains both an under- and an over-approximation module. The approximations are refined in an automatic manner by information flow between the two modules. The technique implemented by TRAU can handle a rich class of string constraints and has better performance than state-of-the-art string solvers.

  • 19.
    Abdullah Al Ahad, Muhammed
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Non-linearstates in parallel Blasius boundary layer2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    There is large theoretical, experimental and numerical interest in studying boundary layers, which develop around any body moving through a fluid. The simplest of these boundary layers lead to the theoretical abstraction of a so-called Blasius boundary layer, which can be derived under the assumption of a flat plate and zero external pressure gradient. The Blasius solution is characterised by a slow growth of the boundary layer in the streamwise direction. For practical purposes, in particular related to studying transition scenarios, non-linear finite-amplitude states (exact coherent states, edge states), but also for turbulence, a major simplification of the problem could be attained by removing this slow streamwise growth, and instead consider a parallel boundary layer. Parallel boundary layers are found in reality, e.g. when applying suction (asymptotic suction boundary layer) or rotation (Ekman boundary layer), but not in the Blasius case. As this is only a model which is not an exact solution to the Navier-Stokes (or boundary-layer) equations, some modifications have to be introduced into the governing equations in order for such an approach to be feasible. Spalart and Yang introduced a modification term to the governing Navier-Stokes equations in 1987. In this thesis work, we adapted the amplitude of the modification term introduced by Spalart and Yang to identify the nonlinear states in the parallel Blasius boundary layer. A final application of this modification was in determining the so-called edge states for boundary layers, previously found in the asymptotic suction boundary layer

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  • 20.
    Abdulle, Assyr
    et al.
    Institute of Mathematics, Ecole Polytechnique Federale de Lausanne, Switzerland.
    Arjmand, Doghonay
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Paganoni, Edoardo
    Institute of Mathematics, Ecole Polytechnique Federale de Lausanne, Switzerland.
    A parabolic local problem with exponential decay of the resonance error for numerical homogenization2021In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 31, no 13, article id 2733-2772Article in journal (Refereed)
    Abstract [en]

    This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro-macro coupling, where the macromodel describes the coarse scale behaviour, and the micro model is solved only locally to upscale the effective quantities, which are missing in the macro model. The fact that the micro problems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first order error in ε/δ, where ε < δ represents the characteristic length ofthe small scale oscillations and δ^d is the size of micro domain. This error dominates all other errors originating from the discretization of the macro and the micro problems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of the present work is to analyse a parabolic approach, first announced in [A. Abdulle,D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019], for computing the homogenized coefficients with arbitrarily high convergence rates in ε/δ. The analysis covers the setting of periodic microstructure,and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic micro structures.

  • 21.
    Abdulle, Assyr
    et al.
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    Arjmand, Doghonay
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    Paganoni, Edoardo
    Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Station 8, Lausanne,CH-1015, Switzerland.
    A parabolic local problem with exponential decay of the resonance error for numerical homogenization2021In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 31, no 13, p. 2733-2772Article in journal (Refereed)
    Abstract [en]

    This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro–macro-coupling, where the macromodel describes the coarse scale behavior, and the micromodel is solved only locally to upscale the effective quantities, which are missing in the macromodel. The fact that the microproblems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first-order error in 𝜀/𝛿𝜀/δ, where 𝜀<𝛿𝜀<δ represents the characteristic length of the small scale oscillations and 𝛿𝑑δd is the size of microdomain. This error dominates all other errors originating from the discretization of the macro and the microproblems, and its reduction is a main issue in today’s engineering multiscale computations. The objective of this work is to analyze a parabolic approach, first announced in A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019, for computing the homogenized coefficients with arbitrarily high convergence rates in 𝜀/𝛿𝜀/δ. The analysis covers the setting of periodic microstructure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. non-periodic microstructures.

  • 22.
    Abdulle, Assyr
    et al.
    Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    Arjmand, Doghonay
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    Paganoni, Edoardo
    Ecole Polytech Fed Lausanne, Inst Math, ANMC, Stn 8, Lausanne, Switzerland..
    AN ELLIPTIC LOCAL PROBLEM WITH EXPONENTIAL DECAY OF THE RESONANCE ERROR FOR NUMERICAL HOMOGENIZATION2023In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 21, no 2, p. 513-541Article in journal (Refereed)
    Abstract [en]

    Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These effective data need to be computed by running local microscale simulations followed by a local averaging of the microscopic information. Motivated by the classical homogenization theory, it is a common practice to use local elliptic cell problems for computing the missing homogenized coefficients in the macro model. Such a consideration results in a first order error O(E/8), where E represents the wavelength of the microscale variations and 8 is the size of the microscopic simulation boxes. This error, called ``resonance error,"" originates from the boundary conditions used in the microproblem and typically dominates all other errors in a multiscale numerical method. Optimal decay of the resonance error remains an open problem, although several interesting approaches reducing the effect of the boundary have been proposed over the last two decades. In this paper, as an attempt to resolve this problem, we propose a computationally efficient, fully elliptic approach with exponential decay of the resonance error.

  • 23.
    Abdulle, Assyr
    et al.
    École polytechnique fédérale de Lausanne, Switzerland.
    Arjmand, Doghonay
    École polytechnique fédérale de Lausanne, Switzerland.
    Paganoni, Edoardo
    École polytechnique fédérale de Lausanne, Switzerland.
    Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems2019In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, no 6, p. 545-551Article in journal (Refereed)
    Abstract [en]

    This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.

  • 24. Abdulle, Assyr
    et al.
    Arjmand, Doghonay
    Paganoni, Edoardo
    Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems2019In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 357, no 6, p. 545-551Article in journal (Refereed)
    Abstract [en]

    This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.

  • 25.
    Abdulle, Assyr
    et al.
    ANMC, EPFL.
    Cohen, David
    Institut für Angewandte und Numerische Mathematik, KIT.
    Vilmart, Gilles
    ANMC, EPFL.
    Konstantinos, Zygalakis
    ANMC, EPFL.
    High weak order methods for stochastic differential equations based on modified equations2012In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 3, p. A1800-A1823Article in journal (Refereed)
    Abstract [en]

    Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (mean-square stable) stochastic problems, and implicit integrators that exactly conserve all quadratic firstintegrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

  • 26.
    Abedin, Arian
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ligai, Wolmir
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Automatingand optimizing pile group design using a Genetic Algorithm2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In bridge design, a set of piles is referred to as a pile group. The design process of pile groups employed by many firms is currently manual, time consuming, and produces pile groups that are not robust against placement errors.

    This thesis applies the metaheuristic method Genetic Algorithm to automate and improve the design of pile groups for bridge column foundations. A software is developed and improved by implementing modifications to the Genetic Algorithm. The algorithm is evaluated by the pile groups it produces, using the Monte Carlo method to simulate errors for the purpose of testing the robustness. The results are compared with designs provided by the consulting firm Tyrens AB.

    The software is terminated manually, and generally takes less than half an hour to produce acceptable pile groups. The developed Genetic Algorithm Software produces pile groups that are more robust than the manually designed pile groups to which they are compared, using the Monte Carlo method. However, due to the visually disorganized designs, the pile groups produced by the algorithm may be di cult to get approved by Trafikverket. The software might require further modifications addressing this problem before it can be of practical use.

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  • 27.
    Abenius, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain2005Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Numerical simulation is an important tool in understanding the electromagnetic field and how it interacts with the environment. Different topics for time-domain finite-difference (FDTD) and finite-element (FETD) methods for Maxwell's equations are treated in this thesis.

    Subcell models are of vital importance for the efficient modeling of small objects that are not resolved by the grid. A novel model for thin sheets using shell elements is proposed. This approach has the advantage of taking into account discontinuities in the normal component of the electric field, unlike previous models based on impedance boundary conditions (IBCs). Several results are presented to illustrate the capabilities of the shell element approach.

    Waveguides are of fundamental importance in many microwave applications, for example in antenna feeds. The key issues of excitation and truncation of waveguides are addressed. A complex frequency shifted form of the uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) in FETD is developed. Prism elements are used to promote automatic grid generation and enhance the performance. Results are presented where reflection errors below -70dB are obtained for different types of waveguides, including inhomogeneous cases. Excitation and analysis via the scattering parameters are achieved using waveguide modes computed by a general frequency-domain mode solver for the vector Helmholtz equation. Huygens surfaces are used in both FDTD and FETD for excitation in waveguide ports.

    Inverse problems have received an increased interest due to the availability of powerful computers. An important application is non-destructive evaluation of material. A time-domain, minimization approach is presented where exact gradients are computed using the adjoint problem. The approach is applied to a general form of Maxwell's equations including dispersive media and UPML. Successful reconstruction examples are presented both using synthetic and experimental measurement data. Parameter reduction of complex geometries using simplified models is an interesting topic that leads to an inverse problem. Gradients for subcell parameters are derived and a successful reconstruction example is presented for a combined dielectric sheet and slot geometry.

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  • 28. Abenius, Erik
    et al.
    Andersson, Ulf
    Edelvik, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Eriksson, Lasse
    Ledfelt, Gunnar
    Hybrid time domain solvers for the Maxwell equations in 2D2002In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 53, p. 2185-2199Article in journal (Refereed)
  • 29.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edelvik, Fredrik
    Thin Sheet Modeling Using Shell Elements in the Finite-Element Time-Domain Method2006In: IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, E-ISSN 1558-2221, Vol. 54, p. 28-34Article in journal (Refereed)
  • 30.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Edelvik, Fredrik
    Johansson, Christer
    Waveguide Truncation Using UPML in the Finite-Element Time-Domain Method2005Report (Other academic)
    Abstract [en]

    An important part of numerical waveguide modeling is the termination of the waveguide using artificial boundaries. In this paper we develop a perfectly matched layer (PML) for waveguides in the finite-element time-domain method (FETD). The PML is discretized by prism elements aligned with the direction of propagation of the waveguide. Assuming that the waveguide is discretized by tetrahedra such a grid is easily generated from a cross-sectional surface in the waveguide. The proposed method has the advantage of being general with regard to the geometry and material of the waveguide. Previous works on PML for FETD have reported problems with late-time instability. While still present in the current approach, our results indicate that the instability is less severe for the prism element PML compared to a tetrahedral PML. Moreover, it may be controlled by increasing the number of grid points in the absorbing layer. It should be noted that the instability appears long after the energy has been attenuated and therefore pose no problems in practical computations. The performance of the suggested scheme is demonstrated for several waveguide problems, including an inhomogeneous case.

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  • 31.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Johansson, Christer
    A General Approach for Time-Domain Simulation of Waveguides in 3D2004In: Proc. EMB 04, Computational Electromagnetics: Methods and Applications, Göteborg, Sweden: Department of Electromagnetics, Chalmers University of Technology , 2004, p. 220-226Conference paper (Other academic)
  • 32.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Johansson, Christer
    Modeling of inhomogeneous waveguides using hybrid methods2005Manuscript (preprint) (Other academic)
  • 33.
    Abenius, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Strand, Bo
    Solving inverse electromagnetic problems using FDTD and gradient-based minimization2006In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 68, p. 650-673Article in journal (Refereed)
  • 34. Abenius, Erik
    et al.
    Strand, Bo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Alestra, Stephane
    Inverse Electromagnetic Scattering Using the Finite-Difference Time-Domain Method2000In: Proc. Millennium Conference on Antennas and Propagation, Noordwijk, The Netherlands: ESA Publications , 2000, p. 4-Conference paper (Refereed)
  • 35.
    Abgrall, Remi
    et al.
    Institute of Mathematics, University of Zurich, Switzerland.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa.
    Öffner, Philipp
    Institute of Mathematics, University of Zurich, Switzerland. Institute of Mathematics, Johannes Gutenberg-Universtiy, Germany.
    Tokareva, Svetlana
    Theoretical Division, Applied Mathematics and Plasma Physics Group (T-5), Los Alamos National Laboratory, USA.
    Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems2020In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 85, no 2, article id 43Article in journal (Refereed)
    Abstract [en]

    In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

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  • 36.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Anguzu, Collins
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Mango, John Magero
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Kakuba, Gudwin
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A Variant of Updating Page Rank in Evolving Tree graphs2019In: Proceedings of 18th Applied Stochastic Models and Data Analysis International Conference with the Demographics 2019 Workshop, Florence, Italy: 11-14 June, 2019 / [ed] Christos H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2019, p. 31-49Conference paper (Refereed)
    Abstract [en]

    PageRank update refers to the process of computing new PageRank values after change(s) (addition or removal of links/vertices) has occurred in real life networks. The purpose of the updating is to avoid recalculating the values from scratch. To efficiently carry out the update, we consider PageRank as the expected number of visits to target vertex if multiple random walks are performed, starting at each vertex once and weighing each of these walks by a weight value. Hence, it might be looked at as updating non-normalised PageRank. In the proposed approach, a scaled adjacency matrix is sequentially updated after every change and the levels of the vertices being updated as well. This enables sets of internal and sink vertices dependent on their roots or parents, thus vector-vector product can be performed sequentially since there are no infinite steps from one vertex to the other.

  • 37.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John Magero
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A Variant of Updating PageRank in Evolving Tree Graphs2021In: Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis Methods and Tools / [ed] Yannis Dimotikalis, Alex Karagrigoriou, Christina Parpoula, Christos H. Skiadas, John Wiley & Sons, Inc. Hoboken, NJ, USA , 2021, Vol. 7, p. 3-22Chapter in book (Refereed)
    Abstract [en]

    A PageRank update refers to the process of computing new PageRank valuesafter a change(s) (addition or removal of links/vertices) has occurred in real-lifenetworks. The purpose of updating is to avoid re-calculating the values from scratch.To efficiently carry out the update, we consider PageRank to be the expected numberof visits to a target vertex if multiple random walks are performed, starting at eachvertex once and weighing each of these walks by a weight value. Hence, it mightbe looked at as updating a non-normalized PageRank. We focus on networks of treegraphs and propose an approach to sequentially update a scaled adjacency matrix afterevery change, as well as the levels of the vertices. In this way, we can update thePageRank of affected vertices by their corresponding levels.

  • 38.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John Magero
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    PageRank in evolving tree graphs2018In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4-6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Springer, 2018, Vol. 271, p. 375-390Chapter in book (Refereed)
    Abstract [en]

    In this article, we study how PageRank can be updated in an evolving tree graph. We are interested in finding how ranks of the graph can be updated simultaneously and effectively using previous ranks without resorting to iterative methods such as the Jacobi or Power method. We demonstrate and discuss how PageRank can be updated when a leaf is added to a tree, at least one leaf is added to a vertex with at least one outgoing edge, an edge added to vertices at the same level and forward edge is added in a tree graph. The results of this paper provide new insights and applications of standard partitioning of vertices of the graph into levels using breadth-first search algorithm. Then, one determines PageRanks as the expected numbers of random walk starting from any vertex in the graph. We noted that time complexity of the proposed method is linear, which is quite good. Also, it is important to point out that the types of vertex play essential role in updating of PageRank.

  • 39.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Mango, John Magero
    Makerere University, Kampala, Uganda.
    Kakuba, Godwin
    Makerere University, Kampala, Uganda.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Updating of PageRank in Evolving Tree graphs2020In: Data Analysis and Applications 3: Computational, Classification, Financial, Statistical and Stochastic Methods / [ed] A. Makrides, A. Karagrigoriou, C.H. Skiadas, John Wiley & Sons, 2020, p. 35-51Chapter in book (Refereed)
    Abstract [en]

    Summary Updating PageRank refers to a process of computing new PageRank values after changes have occurred in a graph. The main goal of the updating is to avoid recalculating the values from scratch. This chapter focuses on updating PageRank of an evolving tree graph when a vertex and an edge are added sequentially. It describes how to maintain level structures when a cycle is created and investigates the practical and theoretical efficiency to update PageRanks for an evolving graph with many cycles. The chapter discusses the convergence of the power method applied to stochastic complement of Google matrix when a feedback vertex set is used. It also demonstrates that the partition by feedback vertex set improves asymptotic convergence of power method in updating PageRank in a network with cyclic components.

  • 40.
    Abola, Benard
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, School of Physical Sciences, Makerere University, Kampala, Uganda.
    Biganda, Pitos
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Department of Mathematics, College of Natural and Applied Sciences, University of Dar es Salaam,Tanzania.
    Engström, Christopher
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Evaluation of Stopping Criteria for Ranks in Solving Linear Systems2019In: Data Analysis and Applications 1: Clustering and Regression, Modeling‐estimating, Forecasting and Data Mining, Volume 2 / [ed] Christos H. Skiadas, James R. Bozeman, John Wiley & Sons, 2019, Chapter 10, p. 137-152Chapter in book (Refereed)
    Abstract [en]

    Bioinformatics, internet search engines (web pages) and social networks are some of the examples with large and high sparsity matrices. For some of these systems, only the actual ranks of the solution vector is interesting rather than the vector itself. In this case, it is desirable that the stopping criterion reflects the error in ranks rather than the residual vector that might have a lower convergence. This chapter evaluates stopping criteria on Jacobi, successive over relaxation (SOR) and power series iterative schemes. Numerical experiments were performed and results show that Kendall's correlation coefficient gives good stopping criterion of ranks for linear system of equations. The chapter focuses on the termination criterion as means of obtaining good ranks. It outlines some studies carried out on stopping criteria in solving the linear system.

  • 41.
    Abrahamsson, Leif R.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A priori estimates for solutions of singular perturbations with a turning point1977In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590, Vol. 56, p. 51-69Article in journal (Refereed)
  • 42.
    Abrahamsson, Leif R.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Keller, Herbert B.
    Kreiss, Heinz-Otto
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Difference approximations for singular perturbations of systems of ordinary differential equations1974In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 22, p. 367-391Article in journal (Refereed)
  • 43. Aceto, Lidia
    et al.
    Mazza, Mariarosa
    Serra-Capizzano, Stefano
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis2020In: Calcolo, ISSN 0008-0624, E-ISSN 1126-5434, Vol. 57, article id 27Article in journal (Refereed)
  • 44. Achdou, Yves
    et al.
    Dao, Manh Khang
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Ley, Olivier
    Tchou, Nicoletta
    Finite horizon mean field games on networks2020In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 59, no 5, article id 157Article in journal (Refereed)
    Abstract [en]

    We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The value functionuis continuous and satisfies general Kirchhoff conditions at the vertices. The densitymof the distribution of states satisfies dual transmission conditions: in particular,mis generally discontinuous across the vertices, and the values ofmon each side of the vertices satisfy some compatibility conditions. The stress is put on the case when the Hamiltonian is Lipschitz continuous. Existence, uniqueness and regularity results are proven.

  • 45.
    Achieng, Pauline
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Analysis of the Robin-Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains2020Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed.

    We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains.

    We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure.

    In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, μ0 and μ1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, μ0 and μ1 are also chosen appropriately.

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  • 46.
    Achieng, Pauline
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Reconstruction of solutions of Cauchy problems for elliptic equations in bounded and unbounded domains using iterative regularization methods2023Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Cauchy problems for elliptic equations arise in applications in science and engineering. These problems often involve finding important information about an elliptical system from indirect or incomplete measurements. Cauchy problems for elliptic equations are known to be disadvantaged in the sense that a small pertubation in the input can result in a large error in the output. Regularization methods are usually required in order to be able to find stable solutions. In this thesis we study the Cauchy problem for elliptic equations in both bounded and unbounded domains using iterative regularization methods. In Paper I and II, we focus on an iterative regularization technique which involves solving a sequence of mixed boundary value well-posed problems for the same elliptic equation. The original version of the alternating iterative technique is based on iterations alternating between Dirichlet-Neumann and Neumann-Dirichlet boundary value problems. This iterative method is known to possibly work for Helmholtz equation. Instead we study a modified version based on alternating between Dirichlet-Robin and Robin-Dirichlet boundary value problems. First, we study the Cauchy problem for general elliptic equations of second order with variable coefficients in a limited domain. Then we extend to the case of unbounded domains for the Cauchy problem for Helmholtz equation. For the Cauchy problem, in the case of general elliptic equations, we show that the iterative method, based on Dirichlet-Robin, is convergent provided that parameters in the Robin condition are chosen appropriately. In the case of an unbounded domain, we derive necessary, and sufficient, conditions for convergence of the Robin-Dirichlet iterations based on an analysis of the spectrum of the Laplacian operator, with boundary conditions of Dirichlet and Robin types.

    In the numerical tests, we investigate the precise behaviour of the Dirichlet-Robin iterations, for different values of the wave number in the Helmholtz equation, and the results show that the convergence rate depends on the choice of the Robin parameter in the Robin condition. In the case of unbounded domain, the numerical experiments show that an appropriate truncation of the domain and an appropriate choice of Robin parameter in the Robin condition lead to convergence of the Robin-Dirichlet iterations.

    In the presence of noise, additional regularization techniques have to implemented for the alternating iterative procedure to converge. Therefore, in Paper III and IV we focus on iterative regularization methods for solving the Cauchy problem for the Helmholtz equation in a semi-infinite strip, assuming that the data contains measurement noise. In addition, we also reconstruct a radiation condition at infinity from the given Cauchy data. For the reconstruction of the radiation condition, we solve a well-posed problem for the Helmholtz equation in a semi-infinite strip. The remaining solution is obtained by solving an ill-posed problem. In Paper III, we consider the ordinary Helmholtz equation and use seperation of variables to analyze the problem. We show that the radiation condition is described by a non-linear well-posed problem that provides a stable oscillatory solution to the Cauchy problem. Furthermore, we show that the ill–posed problem can be regularized using the Landweber’s iterative method and the discrepancy principle. Numerical tests shows that the approach works well.

    Paper IV is an extension of the theory from Paper III to the case of variable coefficients. Theoretical analysis of this Cauchy problem shows that, with suitable bounds on the coefficients, can iterative regularization methods be used to stabilize the ill-posed Cauchy problem.

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  • 47.
    Achieng, Pauline
    et al.
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering. Univ Nairobi, Kenya.
    Berntsson, Fredrik
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Analysis and Mathematics Education. Linköping University, Faculty of Science & Engineering.
    Robin-Dirichlet alternating iterative procedure for solving the Cauchy problem for Helmholtz equation in an unbounded domain2023In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 31, no 5Article in journal (Refereed)
    Abstract [en]

    We consider the Cauchy problem for the Helmholtz equation with a domain in with N cylindrical outlets to infinity with bounded inclusions in . Cauchy data are prescribed on the boundary of the bounded domains and the aim is to find solution on the unbounded part of the boundary. In 1989, Kozlov and Mazya proposed an alternating iterative method for solving Cauchy problems associated with elliptic, selfadjoint and positive-definite operators in bounded domains. Different variants of this method for solving Cauchy problems associated with Helmholtz-type operators exists. We consider the variant proposed by Berntsson, Kozlov, Mpinganzima and Turesson (2018) for bounded domains and derive the necessary conditions for the convergence of the procedure in unbounded domains. For the numerical implementation, a finite difference method is used to solve the problem in a simple rectangular domain in R-2 that represent a truncated infinite strip. The numerical results shows that by appropriate truncation of the domain and with appropriate choice of the Robin parameters mu(0) and mu(1), the Robin-Dirichlet alternating iterative procedure is convergent.

  • 48.
    Ackleh, Azmy S.
    et al.
    University of Louisiana at Lafayette, USA.
    Lyons, Rainey
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Saintier, Nicolas
    Universidad de Buenos Aires, Argentina.
    High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures2023In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 20, no 7, p. 11805-11820Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop explicit and semi-implicit second-order high-resolution finite difference schemes for a structured coagulation-fragmentation model formulated on the space of Radon measures. We prove the convergence of each of the two schemes to the unique weak solution of the model. We perform numerical simulations to demonstrate that the second order accuracy in the Bounded-Lipschitz norm is achieved by both schemes.

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  • 49. Adams, Henry
    et al.
    Tausz, Andrew
    Vejdemo-Johansson, Mikael
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP. Institut Jozef Stefan, Slovenia .
    javaPlex: A Research Software Package for Persistent (Co) Homology2014Conference paper (Refereed)
    Abstract [en]

    The computation of persistent homology has proven a fundamental component of the nascent field of topological data analysis and computational topology. We describe a new software package for topological computation, with design focus on needs of the research community. This tool, replacing previous jPlex and Plex, enables researchers to access state of the art algorithms for persistent homology, cohomology, hom complexes, filtered simplicial complexes, filtered cell complexes, witness complex constructions, and many more essential components of computational topology. We describe, herewithin, the design goals we have chosen, as well as the resulting software package, and some of its more novel capabilities.

  • 50.
    Adegboye, Oluwatayomi Rereloluwa
    et al.
    Univ Mediterranean Karpasia, Turkiye.
    Feda, Afi Kekeli
    European Univ Lefke, Turkiye.
    Ojekemi, Opeoluwa Seun
    Univ Mediterranean Karpasia, Turkiye.
    Agyekum, Ephraim Bonah
    Ural Fed Univ, Russia.
    Hussien, Abdelazim
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering. Fayoum Univ, Egypt; Appl Sci Private Univ, Jordan; Middle East Univ, Jordan.
    Kamel, Salah
    Aswan Univ, Egypt.
    Chaotic opposition learning with mirror reflection and worst individual disturbance grey wolf optimizer for continuous global numerical optimization2024In: Scientific Reports, E-ISSN 2045-2322, Vol. 14, no 1, article id 4660Article in journal (Refereed)
    Abstract [en]

    The effective meta-heuristic technique known as the grey wolf optimizer (GWO) has shown its proficiency. However, due to its reliance on the alpha wolf for guiding the position updates of search agents, the risk of being trapped in a local optimal solution is notable. Furthermore, during stagnation, the convergence of other search wolves towards this alpha wolf results in a lack of diversity within the population. Hence, this research introduces an enhanced version of the GWO algorithm designed to tackle numerical optimization challenges. The enhanced GWO incorporates innovative approaches such as Chaotic Opposition Learning (COL), Mirror Reflection Strategy (MRS), and Worst Individual Disturbance (WID), and it's called CMWGWO. MRS, in particular, empowers certain wolves to extend their exploration range, thus enhancing the global search capability. By employing COL, diversification is intensified, leading to reduced solution stagnation, improved search precision, and an overall boost in accuracy. The integration of WID fosters more effective information exchange between the least and most successful wolves, facilitating a successful exit from local optima and significantly enhancing exploration potential. To validate the superiority of CMWGWO, a comprehensive evaluation is conducted. A wide array of 23 benchmark functions, spanning dimensions from 30 to 500, ten CEC19 functions, and three engineering problems are used for experimentation. The empirical findings vividly demonstrate that CMWGWO surpasses the original GWO in terms of convergence accuracy and robust optimization capabilities.

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