Efficient Partition-of-Unity Radial-Basis-Function Interpolation for Coupled Problems: Efficient partition-of-unity radial-basis-function interpolation for coupled problems

Authors: David Schneider, Benjamin Uekermann

Source: SIAM Journal on Scientific Computing. 47:B558-B582

Subject Terms: partition-of-unity, Algorithms for approximation of functions, data mapping, radial-basis functions, Numerical interpolation, math software, high-performance computing, multiphysics coupling, Parallel numerical computation

File Description: application/xml

Optimizing Coarse Propagators in Parareal Algorithms: Optimizing coarse propagators in parareal algorithms

Authors: Bangti Jin, Qingle Lin, Zhi Zhou

Source: SIAM Journal on Scientific Computing. 47:A735-A761

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, convergence factor, single step integrator, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, parareal algorithm, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parabolic problems

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.15320
https://zbmath.org/8010023
https://doi.org/10.1137/23m1619733

A Selectively Relaxed Splitting Preconditioning Strategy for the Flux-Limited Multi-Group Radiation Diffusion Equations in Three Dimensions: A selectively relaxed splitting preconditioning strategy for the flux-limited multi-group radiation diffusion equations in three dimensions

Authors: Yue, Xiaoqiang, Zhang, Chenxi, Chen, Chunyan, Xu, Xiaowen, Shu, Shi

Source: East Asian Journal on Applied Mathematics. 15:113-137

Subject Terms: radiation diffusion equation, algebraic multigrid, parallel computing, Numerical methods for partial differential equations, boundary value problems, Preconditioners for iterative methods, Parallel numerical computation, selective relaxation, matrix splitting preconditioner

File Description: application/xml

A Multigrid Reduction Framework for Domains with Symmetries: A multigrid reduction framework for domains with symmetries

Authors: Alsalti Baldellou, Àdel, Janna, Carlo, Álvarez Farré, Xavier, Trias Miquel, Francesc Xavier

Source: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Subject Terms: Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids, FOS: Computer and information sciences, Àrees temàtiques de la UPC::Física::Termodinàmica, Multigrid methods, domain decomposition for boundary value problems involving PDEs, Spatial symmetries, spatial symmetries, Navier-Stokes equations for incompressible viscous fluids, Parallel numerical computation, Numerical Analysis (math.NA), Computational methods for sparse matrices, Poisson's equation, Computer Science - Distributed, Parallel, and Cluster Computing, AMG, multigrid reduction, FOS: Mathematics, Multigrid reduction, Preconditioners for iterative methods, SpMM, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 65F08, 65F50, 65N55, 65Y05

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/abs/2407.05930
https://hdl.handle.net/11577/3552922
https://doi.org/10.1137/24M1638513

New Time Domain Decomposition Methods for Parabolic Optimal Control Problems II: Neumann–Neumann Algorithms: New time domain decomposition methods for parabolic optimal control problems. II: Neumann-Neumann algorithms

Authors: Martin J. Gander, Liu-Di Lu

Source: SIAM Journal on Numerical Analysis. 62:2588-2610

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Controllability, parallel in time, time domain decomposition, 65M12, 65M55, 65Y05, Parallel numerical computation, parabolic optimal control problems, Numerical Analysis (math.NA), PDE constrained optimization (numerical aspects), 01 natural sciences, convergence analysis, Neumann-Neumann algorithm, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, Optimization and Control (math.OC), Approximation by arbitrary linear expressions, Finite difference methods for initial value and initial-boundary value problems involving PDEs, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Optimization and Control

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.15522
https://zbmath.org/7957568
https://doi.org/10.1137/24m1634424

Numerical Approach for Solving Two-Dimensional Time-Fractional Fisher Equation via HABC-N Method

Authors: Liu, Ren^Aff1, Wu, Lifei^{Aff1, IDs4296702300282w_cor1}

Source: Communications on Applied Mathematics and Computation. 7(1):315-346

Development of the Next-generation Atmosphere Dynamics Model in Russia: Current State and Prospects: Development of the next-generation atmosphere dynamics model in Russia: current state and prospects

Authors: Shashkin, V. V., Goyman, G. S., Tretyak, I. D.

Source: Lobachevskii Journal of Mathematics. 45:3159-3172

Subject Terms: Geophysical flows, Computational methods for problems pertaining to geophysics, Finite difference methods for initial value and initial-boundary value problems involving PDEs, numerical weather prediction, Parallel numerical computation, meteorology, Meteorology and atmospheric physics, Euler equations, Finite difference methods applied to problems in fluid mechanics, climate modeling

File Description: application/xml

Access URL: https://zbmath.org/7954500
https://doi.org/10.1134/s1995080224603746

Parallel-in-Time Preconditioner for the Time Spectral Methods: Parallel-in-time preconditioner for the time spectral methods

Authors: Changyang Tang, Shu-Lin Wu, Tao Zhou, Yuancheng Zhou

Source: Journal of Scientific Computing. 103

Subject Terms: diagonalization-based techinique, parallel-in-time preconditioner, Parallel numerical computation, GMRES, time spectral method, spectral analysis, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: https://zbmath.org/8036983
https://doi.org/10.1007/s10915-025-02899-w

A Two-Level Block Preconditioned Jacobi–Davidson Method for Multiple and Clustered Eigenvalues of Elliptic Operators: A two-level block preconditioned Jacobi-Davidson method for multiple and clustered eigenvalues of elliptic operators

Authors: Qigang Liang, Wei Wang, Xuejun Xu

Source: SIAM Journal on Numerical Analysis. 62:998-1019

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite element discretization, multiple and clustered eigenvalues, Rate of convergence, degree of approximation, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, PDE eigenvalue problems, preconditioned Jacobi-Davidson method, overlapping domain decomposition, FOS: Mathematics, Preconditioners for iterative methods, Mathematics - Numerical Analysis, 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2203.06327

A simple regularized forward–backward–forward dynamical system for structured monotone inclusions: A simple regularized forward-backward-forward dynamical system for structured monotone inclusions

Authors: Pham Ky Anh, Trinh Ngoc Hai

Source: Computational and Applied Mathematics. 44

Subject Terms: iterative regularization method, Convex programming, Evolution inclusions, Parallel numerical computation, Monotone operators and generalizations, forward-backward-forward method, dynamical system, Numerical methods for variational inequalities and related problems, structured monotone inclusions

File Description: application/xml

Relaxed Two-Step Inertial Tseng’s Extragradient Method for Nonmonotone Variational Inequalities: Relaxed two-step inertial Tseng's extragradient method for nonmonotone variational inequalities

Authors: Duong Viet Thong, Pham Ky Anh, Vu Tien Dung

Source: Journal of Optimization Theory and Applications. 205

Subject Terms: nonmonotone mapping, Fixed-point theorems, Iterative procedures involving nonlinear operators, Variational and other types of inequalities involving nonlinear operators (general), two step inertial technique, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, weak convergence, Parallel numerical computation, Parallel algorithms in computer science, Tseng's extragradient method, variational inequality, Numerical methods for variational inequalities and related problems

File Description: application/xml

An efficient algorithm with double inertial steps for solving split common fixed point problems and an application to signal processing

Authors: Duong Viet Thong, Simeon Reich, Xiao-Huan Li, Pham Thi Hong Tham

Source: Computational and Applied Mathematics. 44

Subject Terms: Fixed-point theorems, split common fixed point problem, demicontractive operator, Parallel numerical computation, Parallel algorithms in computer science, signal processing, Monotone operators and generalizations, self-adaptive algorithm, Numerical methods for variational inequalities and related problems, double inertial steps

File Description: application/xml

Matrix-Free Parallel Scalable Multilevel Deflation Preconditioning for Heterogeneous Time-Harmonic Wave Problems: Matrix-free parallel scalable multilevel deflation preconditioning for heterogeneous time-harmonic wave problems

Authors: Jinqiang Chen, Vandana Dwarka, Cornelis Vuik

Source: Journal of Scientific Computing. 102

Subject Terms: Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, parallel computing, 65F08, 65Y05, 35J05, Parallel numerical computation, Numerical Analysis (math.NA), CSLP, G.1.0, FOS: Mathematics, scalable, Preconditioners for iterative methods, Helmholtz equation, Mathematics - Numerical Analysis, deflation, matrix-free

File Description: application/xml

Access URL: http://arxiv.org/abs/2412.04980

Communication Avoiding Block Low-Rank Parallel Multifrontal Triangular Solve with Many Right-Hand Sides: Communication avoiding block low-rank parallel multifrontal triangular solve with many right-hand sides

Authors: Amestoy, Patrick, Boiteau, Olivier, Buttari, Alfredo, Gerest, Matthieu, Jézéquel, Fabienne, L’excellent, Jean-Yves, Mary, Theo

Contributors: Mary, Theo, Mumps Technologies Lyon, EDF R&D (EDF R&D), EDF (EDF), Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Performance et Qualité des Algorithmes Numériques (PEQUAN), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Panthéon-Assas

Source: SIAM Journal on Matrix Analysis and Applications. 45:148-166

Subject Terms: block low-rank matrices, linear systems, Numerical methods for low-rank matrix approximation, matrix compression, [MATH] Mathematics [math], Parallel numerical computation, [INFO] Computer Science [cs], Direct numerical methods for linear systems and matrix inversion, communication avoiding algorithms, Computational methods for sparse matrices, LU factorization, low-rank approximations, numerical linear algebra, data sparse matrices, [INFO]Computer Science [cs], triangular solve, [MATH]Mathematics [math]

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/7791523
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1/document
https://doi.org/10.1137/23m1568600
https://hal.science/hal-04082415v1

A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications: A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications

Authors: Liu, Xinyu, Shen, Jie, Zhang, Xiangxiong

Source: Communications in Computational Physics. 36:1157-1185

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Finite difference methods for boundary value problems involving PDEs, FOS: Computer and information sciences, tensor matrix multiplication, rectangular domain, GPU, Parallel numerical computation, spectral element methods, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, direct solver, Computer Science - Distributed, Parallel, and Cluster Computing, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 3D Poisson equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.00226

The parareal algorithm for Caputo-Hadamard fractional differential equations

Authors: He, Tingting, Lu, Jian, Li, Min

Source: Communications on Analysis and Computation. 2:432-453

Subject Terms: auxiliary variables, Volterra integral equations, parareal algorithm, local time-integrators, Parallel numerical computation, Numerical methods for integral equations, Caputo-Hadamard fractional differential equations

File Description: application/xml

A Generalized Selectively Relaxed Matrix Splitting Preconditioning Strategy for Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations: A generalized selectively relaxed matrix splitting preconditioning strategy for three-dimensional flux-limited multi-group radiation diffusion equations

Authors: Yue, Xiaoqiang, Xia, Sheng, Chen, Chunyan, Xu, Xiaowen, Shu, Shi

Source: Numerical Mathematics: Theory, Methods and Applications. 17:630-657

Subject Terms: Multigrid methods, domain decomposition for boundary value problems involving PDEs, algebraic multigrid, matrix splitting preconditioning, Finite volume methods for boundary value problems involving PDEs, radiation diffusion equations, Preconditioners for iterative methods, Parallel numerical computation, selective relaxation, parallel and distributed computing

File Description: application/xml

A parallel domain decomposition-based implicit finite volume lattice Boltzmann method for incompressible thermal convection flows on unstructured grids

Authors: Lei Xu, Rongliang Chen, Linyan Gu, Wu Zhang

Source: Journal of Computational and Applied Mathematics. 465:116578

Subject Terms: Free convection, implicit backward Euler temporal scheme, concentric annulus flow, Particle methods and lattice-gas methods, Diffusive and convective heat and mass transfer, heat flow, Finite volume methods applied to problems in fluid mechanics, Parallel numerical computation, preconditioned Newton-Krylov algorithm, cavity flow

File Description: application/xml

Adaptive double-inertial projection rules for variational inequalities and CFPPs of finite Bregman relative demicontractions and asymptotical nonexpansivity operators

Authors: Lu-Chuan Ceng, Yue Zhang, Liu-Fang Zheng, Xie Wang, Cong-Shan Wang, Hui-Ying Hu

Source: Communications in Nonlinear Science and Numerical Simulation. 146:108763

Subject Terms: Fixed-point theorems, adaptive double-inertial Bregman projection schemes, a pair of VIPs, finite Bregman's relative demicontractions, Parallel numerical computation, Bregman's relative asymptotic nonexpansivity operator, Monotone operators and generalizations, CFPP, Approximation algorithms, Numerical methods for variational inequalities and related problems

File Description: application/xml

Access URL: https://zbmath.org/8026124
https://doi.org/10.1016/j.cnsns.2025.108763

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