A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices

Authors: Bolten, Matthias, Ekström, Sven-Erik, Doctor, 1977, Furci, Isabella, Serra-Capizzano, Stefano

Source: Electronic Transactions on Numerical Analysis. 58:136-163

Subject Terms: Toeplitz matrices, asymptotic distribution of eigenvalues and singular values, numerical solution of discretized equations for boundary value problems involving PDEs, fractional differential equations, Beräkningsvetenskap med inriktning mot numerisk analys, Scientific Computing with specialization in Numerical Analysis

File Description: electronic

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-495825
https://doi.org/10.1553/etna_vol58s136

A Preconditioner for the Grad-Div Stabilized Equal-Order Finite Elements Discretizations of the Oseen Problem: A preconditioner for the grad-div stabilized equal-order finite elements discretizations of the Oseen problem

Authors: Yunhui He, Maxim Olshanskii

Source: SIAM Journal on Scientific Computing. 47:A1486-A1506

Subject Terms: preconditioning, field-of-values, Krylov subspace methods, FOS: Mathematics, Preconditioners for iterative methods, Oseen problem, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 65F08, 65N22, 65N30, Numerical solution of discretized equations for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, equal-order finite elements

File Description: application/xml

Access URL: http://arxiv.org/abs/2407.07498
https://zbmath.org/8037165
https://doi.org/10.1137/24m1675849

Frequency Range of a Non-Lipschitz Parametric Optimization of a Noise Absorption: Frequency range of a non-Lipschitz parametric optimization of a noise absorption

Authors: Frédéric Magoulès, Mathieu Menoux, Anna Rozanova-Pierrat

Source: SIAM Journal on Control and Optimization. 63:1267-1285

Subject Terms: Linear equations (linear algebraic aspects), Iterative numerical methods for linear systems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Boundary value problems for second-order elliptic equations, sound absorption, wave propagation, \(d\)-upper regular measure, parametric shape optimization, Helmholtz equation, Numerical solution of discretized equations for boundary value problems involving PDEs, Robin boundary condition, First-order hyperbolic systems

File Description: application/xml

Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with fractional Laplacian and variable coefficient wave number μ: Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with fractional Laplacian and variable coefficient wave number \(\mu \)

Authors: Adriani A., Sormani R. L., Tablino Possio C., Krause R., Serra-Capizzano S.

Source: Linear Algebra and its Applications. 708:551-584

Subject Terms: generalized locally Toeplitz sequences, Eigenvalues, singular values, and eigenvectors, fractional derivatives, Beräkningsmatematik, singular value and eigenvalue asymptotics, Fractional derivatives, Spectral symbol, Preconditioning, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Fractional partial differential equations, Clustering, Computational Mathematics, preconditioning, Generalized locally Toeplitz sequences, Helmholtz equations, Singular value and eigenvalue asymptotics, Toeplitz operators, Hankel operators, Wiener-Hopf operators, FOS: Mathematics, Preconditioners for iterative methods, Mathematics - Numerical Analysis, spectral symbol, 65F08, 35R11, 65N22, 15A18, 47B35, clustering

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2402.10569
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-546221

A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains: A scalable two-level domain decomposition eigensolver for periodic Schrödinger eigenstates in anisotropically expanding domains

Authors: Lambert Theisen, Benjamin Stamm

Source: SIAM Journal on Scientific Computing. 46:A3067-A3093

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, FOS: Computer and information sciences, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Iterative numerical methods for linear systems, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite element method, Schrödinger equation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, coarse spaces, Computational Engineering, Finance, and Science (cs.CE), domain decomposition, preconditioning, FOS: Mathematics, iterative methods, 65N25, 65F15, 65N30, 65F10, 65N22, 65N55, 65F08, Preconditioners for iterative methods, Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.08757

A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments: A posteriori error analysis for a coupled Stokes-poroelastic system with multiple compartments

Authors: Ivan Fumagalli, Nicola Parolini, Marco Verani

Source: J Sci Comput
Journal of Scientific Computing

Subject Terms: J.2, J.3, G.1.8, fluid-poromechanics interaction, Numerical Analysis (math.NA), Stability and convergence of numerical methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Physiological flows, cerebrospinal fluid, Article, multiple-network poroelasticity, FOS: Mathematics, a posteriori estimates, Mathematics - Numerical Analysis, 65N15, 65N22, 65N30, 76Z05

File Description: application/xml

Access URL: https://pubmed.ncbi.nlm.nih.gov/40065827
http://arxiv.org/abs/2407.09659

Adaptive finite volume schemes for anisotropic heterogeneous diffusion problems on arbitary convex and nonconvex meshes

Authors: Zaroual Bazirha, Lahcen Azrar, Ateq Ahmed AlGhamedi

Source: Computational and Applied Mathematics. 44

Subject Terms: discrete duality finite volume (DDFV), Finite volume methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, non-convex mesh, refinement, Numerical solution of discretized equations for boundary value problems involving PDEs, diffusion problems

File Description: application/xml

Hierarchical Interpolative Factorization for Self Green’s Function in 3D Modified Poisson-Boltzmann Equations: Hierarchical interpolative factorization for self Green's function in 3D modified Poisson-Boltzmann equations

Authors: Yihui Tu, Zhenli Xu, Haizhao Yang

Source: Communications on Applied Mathematics and Computation. 7:536-561

Subject Terms: Computational methods for sparse matrices, self Green's function, modified Poisson-Boltzmann (MPB) equations, hierarchical interpolative factorization, FOS: Physical sciences, Numerical solution of discretized equations for boundary value problems involving PDEs, Computational Physics (physics.comp-ph), linear scaling, Physics - Computational Physics, Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics, selected inversion

File Description: application/xml

Access URL: http://arxiv.org/abs/2307.01060
https://zbmath.org/8034289
https://doi.org/10.1007/s42967-023-00352-z

Deep Neural Network for Solving Differential Equations Motivated by Legendre-Galerkin Approximation: Deep neural network for solving differential equations motivated by Legendre-Galerkin approximation

Authors: Chudomelka, Bryce, Hong, Youngjoon, Morgan, John, Kim, Hyunwoo, Park, Jinyoung

Source: International Journal of Numerical Analysis and Modeling. 21:652-673

Subject Terms: data driven numerical method, Numerical algorithms for specific classes of architectures, neural network, deep learning, spectral element method, Legendre-Galerkin method, Spectral, collocation and related methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Computational aspects of data analysis and big data, Artificial neural networks and deep learning

File Description: application/xml

Access URL: https://zbmath.org/7954065
https://doi.org/10.4208/ijnam2024-1026

SlabLU: a two-level sparse direct solver for elliptic PDEs

Authors: Anna Yesypenko, Per-Gunnar Martinsson

Source: Advances in Computational Mathematics. 50

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Numerical Analysis, Random matrices (algebraic aspects), GPU, Numerical methods for low-rank matrix approximation, matrix compression, high-order discretization, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, multifrontal solver, 01 natural sciences, Factorization of matrices, direct solver, Computational methods for sparse matrices, Numerical algorithms for specific classes of architectures, Boundary value problems for second-order elliptic equations, sparse direct solver, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, randomized linear algebra, Helmholtz equation, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2211.07572

An immersed interface neural network for elliptic interface problems

Authors: Zhang, Xinru, He, Qiaolin

Source: Journal of Computational and Applied Mathematics. 459:116372

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Stokes interface problems, immersed interface method, elliptic interface problems, Poisson interface problem, Numerical solution of discretized equations for boundary value problems involving PDEs, neural networks, Artificial neural networks and deep learning

File Description: application/xml

Access URL: https://zbmath.org/7968683
https://doi.org/10.1016/j.cam.2024.116372

Improve the ill-conditioning for small physical covers by area normalized method in numerical manifold method (NMM)

Authors: Yan, Pengfei, Cai, Yongchang, Wu, Jie

Source: Engineering Analysis with Boundary Elements. 139:192-207

Subject Terms: ill-conditioning, area normalized, preconditioning, Numerical methods for partial differential equations, boundary value problems, 0211 other engineering and technologies, numerical manifold method (NMM), local pixel representation, 02 engineering and technology, Numerical solution of discretized equations for boundary value problems involving PDEs, small-physical-cover trouble (ST), 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/7511120
https://doi.org/10.1016/j.enganabound.2022.03.028

An Explicit Exponential Integrator Based on Faber Polynomials and its Application to Seismic Wave Modeling: An explicit exponential integrator based on Faber polynomials and its application to seismic wave modeling

Authors: Fernando V. Ravelo, Pedro S. Peixoto, Martin Schreiber

Source: Journal of Scientific Computing. 98

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Faber polynomial, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Error bounds for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), absorbing boundaries, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, exponential integrator, eigenvalue distribution, Galactic and stellar structure, wave equation, PDEs in connection with astronomy and astrophysics

File Description: application/xml

Access URL: https://zbmath.org/7788954
https://doi.org/10.1007/s10915-023-02413-0

A mixed finite element method for solving coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term

Authors: Mohammad Reza Eslahchi, Maryam Parvizi, Amirreza Khodadadian

Source: Mathematical Methods in the Applied Sciences. 44:12500-12521

Subject Terms: Finite element method, convergence, Raviart-Thomas mixed finite element, Second-order wave equations, Nonlinear boundary, Coupled wave equations, Nonlinear equations, Mixed finite element approximation, Damping, 01 natural sciences, Dewey Decimal Classification::500 | Naturwissenschaften::510 | Mathematik, Wave equations, 65N15 error bounds for boundary value problems involving PDEs, nonlinear wave equation, Numerical approximations, 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs, semi-discretization, Mixed finite element methods, Numerical methods, Space discretizations, Raviart-Thomas mixed finite elements, 0101 mathematics

Access URL: https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mma.7556
https://www.authorea.com/users/310863/articles/441603-a-mixed-finite-element-method-for-solving-coupled-wave-equation-of-kirchhofftype-with-nonlinear-boundary-damping-and-memory-term
https://onlinelibrary.wiley.com/doi/full/10.1002/mma.7556

Randomized compression of rank-structured matrices accelerated with graph coloring

Authors: James Levitt, Per-Gunnar Martinsson

Source: Journal of Computational and Applied Mathematics. 451:116044

Subject Terms: Random matrices (algebraic aspects), HODLR matrix, Numerical linear algebra, Randomized algorithms, hierarchically block separable matrix, Boundary element methods for boundary value problems involving PDEs, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, 01 natural sciences, Factorization of matrices, Computational methods for sparse matrices, hierarchically semiseparable matrix, rank-structured matrices, randomized approximation of matrices, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, 65N22, 65N38, 15A23, 15A52, fast direct solver

File Description: application/xml

Access URL: http://arxiv.org/abs/2205.03406

Interconnected Hierarchical Structures for Fast Direct Elliptic Solution: Interconnected hierarchical structures for fast direct elliptic solution

Authors: Liu, Xiao, Xia, Jianlin, de Hoop, Maarten V., Ou, Xiaofeng

Source: Journal of Scientific Computing. 91

Subject Terms: Complexity and performance of numerical algorithms, neighbor tree, fast sparse direct solver, basis reuse, elliptic equation, Schur complement update, Numerical solution of discretized equations for boundary value problems involving PDEs, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, interconnected hierarchical structure, 01 natural sciences

File Description: application/xml

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

Authors: Gustavo Chávez, George Turkiyyah, Stefano Zampini, David Keyes

Contributors: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Computer Science Program, Extreme Computing Research Center, Applied Mathematics and Computational Science Program, American University of Beirut, Beirut, Lebanon

Source: Journal of Computational and Applied Mathematics. 344:760-781

Subject Terms: hierarchical matrices, Hierarchical matrices, Numerical and Computational Mathematics, math.NA, Numerical and computational mathematics, Applied Mathematics, Numerical & Computational Mathematics, Preconditioning, Parallel numerical computation, Numerical Analysis (math.NA), Numerical solution of discretized equations for boundary value problems involving PDEs, Applied mathematics, 01 natural sciences, Mathematical Sciences, preconditioning, FOS: Mathematics, Preconditioners for iterative methods, Cyclic reduction, Mathematics - Numerical Analysis, Electrical and Electronic Engineering, 0101 mathematics, cyclic reduction, Theory of computation

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/1712.08872
https://escholarship.org/uc/item/0vg3t8v5

A mixed finite element method for solving coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term

Authors: Parvizi, Maryam, Khodadadian, Amirreta, Eslahchi, M.R.

Source: Mathematical Methods in the Applied Sciences 44 (2021), Nr. 17 ; Mathematical Methods in the Applied Sciences

Subject Terms: 65N15 error bounds for boundary value problems involving PDEs, 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs, convergence, nonlinear wave equation, Raviart-Thomas mixed finite element, semi-discretization, Damping, Nonlinear equations, Numerical methods, Wave equations, Coupled wave equations, Mixed finite element approximation, Mixed finite element methods, Nonlinear boundary, Numerical approximations, Raviart-Thomas mixed finite elements, Second-order wave equations, Space discretizations, Finite element method, ddc:510

Relation: ESSN:1099-1476; http://dx.doi.org/10.15488/12382

Availability: https://www.repo.uni-hannover.de/handle/123456789/12481
https://doi.org/10.15488/12382

Hierarchical preconditioning for the stochastic Galerkin method: Upper bounds to the strengthened CBS constants: Hierarchical preconditioning for the stochastic Galerkin method: upper bounds to the strengthened CBS constants

Authors: Ivana Pultarová

Source: Computers & Mathematics with Applications. 71:949-964

Subject Terms: algebraic multilevel iterative method, Multigrid methods, domain decomposition for boundary value problems involving PDEs, preconditioning, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Numerical solution of discretized equations for boundary value problems involving PDEs, 0101 mathematics, stochastic Galerkin method, 01 natural sciences, Computational methods for stochastic equations (aspects of stochastic analysis), Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs, strengthened Cauchy-Bunyakowsky-Schwarz constant, 3. Good health

File Description: application/xml

One-block method for computing the generalized stress intensity factors for Laplace’s equation on a square with a slit and on an L-shaped domain: One-block method for computing the generalized stress intensity factors for Laplace's equation on a square with a slit and on an L-shaped domain

Authors: A. A. Dosiyev, S. C. Buranay

Source: Journal of Computational and Applied Mathematics. 289:400-411

Subject Terms: corner singularity, Fracture and damage, block method, 13. Climate action, Laplace equation, Numerical solution of discretized equations for boundary value problems involving PDEs, stress intensity factor, 0101 mathematics, Other numerical methods in solid mechanics, 01 natural sciences, 7. Clean energy

File Description: application/xml

Access URL: https://zbmath.org/6454478
https://doi.org/10.1016/j.cam.2014.11.029
https://www.sciencedirect.com/science/article/pii/S0377042714005081
https://www.sciencedirect.com/science/article/abs/pii/S0377042714005081
https://dblp.uni-trier.de/db/journals/jcam/jcam289.html#DosiyevB15
https://dialnet.unirioja.es/servlet/articulo?codigo=5277489