Search Results - 65N25: Numerical methods for eigenvalue problems for boundary value problems involving PDEs*

Adaptive Finite Element Approximations of the First Eigenpair Associated with \({p}\)-Laplacian: Adaptive finite element approximations of the first eigenpair associated with \(p\)-Laplacian

Authors: Guanglian Li Jing Li Julie Merten et al.

Source: SIAM Journal on Scientific Computing. 47:A374-A402

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, convergence, Error bounds for boundary value problems involving PDEs, 65N12, 65N25, 65N30, 65N50, 35P30, p-Laplacian, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, adaptive finite element method, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, \(p\)-Laplacian, FOS: Mathematics, Mathematics - Numerical Analysis, Quasilinear elliptic equations with \(p\)-Laplacian, first eigenvalue, a posteriori error estimator

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Access URL: http://arxiv.org/abs/2402.06889
https://zbmath.org/7988245
https://doi.org/10.1137/24m1637052
https://hdl.handle.net/11370/38fde517-5607-4324-a94f-59f28f4250e0
https://doi.org/10.1137/24M1637052
https://research.rug.nl/en/publications/38fde517-5607-4324-a94f-59f28f4250e0

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

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

Tensor Neural Network and Its Numerical Integration: Tensor neural network and its numerical integration

Authors: Wang, Yifan Xie, Hehu Jin, Pengzhan

Source: Journal of Computational Mathematics. 42:1714-1742

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, fixed quadrature points, 02 engineering and technology, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, high-dimensional eigenvalue problem, machine learning, numerical integration, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, Acceleration of convergence in numerical analysis, tensor neural network, 65N30, 65N25, 65L15, 65B99

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Access URL: http://arxiv.org/abs/2207.02754

Computing eigenvalues of the Laplacian on rough domains

Authors: Rösler, Frank Stepanenko, Alexei

Source: Mathematics of Computation. 93:111-161

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, finite element method, eigenvalues, Elliptic operators and their generalizations, Estimates of eigenvalues in context of PDEs, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 35P15, 65N25, 01 natural sciences, Mathematics - Spectral Theory, Fractals, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Spectral Theory (math.SP), Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2104.09444

Symmetrized Two-Scale Finite Element Discretizations for Partial Differential Equations with Symmetric Solutions: Symmetrized two-scale finite element discretizations for partial differential equations with symmetric solutions

Authors: Pengyu Hou Fang Liu Aihui Zhou

Source: Computational Methods in Applied Mathematics. 24:887-908

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, symmetric, two-scale, Error bounds for boundary value problems involving PDEs, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, 01 natural sciences, 65N15, 65N25, 65N30, 65N50, finite element, partial differential equation, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, postprocessed

File Description: application/xml

Access URL: http://arxiv.org/abs/2205.15524

A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains: A quasi-optimal factorization preconditioner for periodic Schrödinger eigenstates in anisotropically expanding domains

Authors: Benjamin Stamm Lambert Theisen

Source: SIAM Journal on Numerical Analysis. 60:2508-2537

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, preconditioner, iterative eigenvalue solvers, Asymptotic behavior of solutions to PDEs, factorization principle, directional homogenization, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Homogenization in context of PDEs, PDEs in media with periodic structure, 01 natural sciences, asymptotic eigenvalue analysis, Computational Engineering, Finance, and Science (cs.CE), periodic Schrödinger equation, FOS: Mathematics, Mathematics - Numerical Analysis, 65N25, 65F15, 65N30, 35B27, 35B40, 0101 mathematics, Computer Science - Computational Engineering, Finance, and Science

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Access URL: http://arxiv.org/abs/2110.14982

Domain decomposition methods for eigenvalue problems

Authors: Lui, SH

Source: Journal of Computational and Applied Mathematics. 117:17-34

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Iterative numerical methods for linear systems, Fictitious domain, Multigrid methods, domain decomposition for boundary value problems involving PDEs, convergence, Applied Mathematics, 65N55, Eigenvalue, 65N25, Estimates of eigenvalues in context of PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Eigenvalue* Schwarz alternating method, 01 natural sciences, fictitious domain, domain inbedding, domain decomposition, Computational Mathematics, Domain imbedding, eigenvalue, Domain decomposition, 0101 mathematics, numerical experiments, Schwarz alternating method

File Description: application/xml

Access URL: https://zbmath.org/1455703
https://doi.org/10.1016/s0377-0427(99)00326-x
https://www.sciencedirect.com/science/article/pii/S037704279900326X
http://repository.ust.hk/ir/Record/1783.1-24385
https://dialnet.unirioja.es/servlet/articulo?codigo=700086
https://www.math.umanitoba.ca/research/bibtexbrowser.php?key=MR1752860&bib=biblio_Lui_Shaun.bib
https://www.sciencedirect.com/science/article/abs/pii/S037704279900326X

A hierarchical method for obtaining eigenvalue enclosures

Authors: Davies, E B

Source: Mathematics of Computation. 69:1435-1456

Subject Terms: Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, 49R10, spectral enclosures, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Estimates of eigenvalues in context of PDEs, 65N25, interval arithmetic, 01 natural sciences, spectrum, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Sturm-Liouville operator, 34L15, FOS: Mathematics, 0101 mathematics, 65L70, Spectral Theory (math.SP), Error bounds for numerical methods for ordinary differential equations, Temple-Lehmann method, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, eigenvalues, 65L15, Rayley-Ritz method, 35P15, 49R05, 65L60, Numerical solution of eigenvalue problems involving ordinary differential equations, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: https://www.ams.org/mcom/2000-69-232/S0025-5718-00-01238-2/S0025-5718-00-01238-2.pdf
http://arxiv.org/abs/math/9803075
https://www.ams.org/journals/mcom/2000-69-232/S0025-5718-00-01238-2/home.html
http://ui.adsabs.harvard.edu/abs/2000MaCom..69.1435D/abstract
https://kclpure.kcl.ac.uk/portal/en/publications/a-hierarchical-method-for-obtaining-eigenvalue-enclosures(9cf25ec8-2c1f-4d32-ad00-791c2973538f).html
https://dblp.uni-trier.de/db/journals/moc/moc69.html#Davies00
https://www.ams.org/mcom/2000-69-232/S0025-5718-00-01238-2/S0025-5718-00-01238-2.pdf

Range of the First Three Eigenvalues of the Planar Dirichlet Laplacian: Range of the first three eigenvalues of the planar Dirichlet Laplacian

Authors: Rustem Yagudin Michael Levitin

Source: LMS Journal of Computation and Mathematics. 6:1-17

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, isoperimetric estimates, 35P15 (Primary), a priori estimates, eigenvalues, Estimates of eigenvalues in context of PDEs, 65N25 (Secondary), Dirichlet Laplacian, Numerical Analysis (math.NA), 01 natural sciences, bounded domain, Mathematics - Spectral Theory, FOS: Mathematics, universal estimates, Mathematics - Numerical Analysis, 0101 mathematics, Spectral Theory (math.SP)

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/EBE749E68828A43CD74082DF9A21A62F/S1461157000000346a.pdf/div-class-title-range-of-the-first-three-eigenvalues-of-the-planar-dirichlet-laplacian-div.pdf
http://arxiv.org/abs/math/0203231
https://zbmath.org/2116744
https://doi.org/10.1112/s1461157000000346
https://www.cambridge.org/core/journals/lms-journal-of-computation-and-mathematics/article/range-of-the-first-three-eigenvalues-of-the-planar-dirichlet-laplacian/EBE749E68828A43CD74082DF9A21A62F
https://researchportal.hw.ac.uk/en/publications/range-of-the-first-three-eigenvalues-of-the-planar-dirichlet-lapl

Galerkin eigenvector approximations

Authors: Christopher Beattie

Source: Mathematics of Computation. 69:1409-1435

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, 65N25, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, 01 natural sciences, sep, Mathematics - Spectral Theory, Numerical solutions to equations with linear operators, spectral methods, FOS: Mathematics, eigenvalue, finite element methods, Mathematics - Numerical Analysis, 0101 mathematics, Petrov-Galerkin methods, Spectral Theory (math.SP), Numerical methods for eigenvalue problems for boundary value problems involving PDEs, convergence, 65F15, 65N30, eigenvector asymptotics, Hilbert space, Numerical Analysis (math.NA), Galerkin approximation, eigenvector, Eigenvalue problems for linear operators, linear operator

File Description: application/xml

Access URL: https://www.ams.org/mcom/2000-69-232/S0025-5718-00-01181-9/S0025-5718-00-01181-9.pdf
http://arxiv.org/abs/math/9805028
https://www.jstor.org/stable/2585074
https://dblp.uni-trier.de/db/journals/moc/moc69.html#Beattie00
https://doi.org/10.1090/S0025-5718-00-01181-9
https://www.ams.org/mcom/2000-69-232/S0025-5718-00-01181-9/S0025-5718-00-01181-9.pdf
https://ui.adsabs.harvard.edu/abs/1998math......5028B/abstract
https://www.ams.org/journals/mcom/2000-69-232/S0025-5718-00-01181-9/home.html

Solving High-Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators.

Authors: Wang, Yifan Lin, Zhongshuo Liao, Yangfei et al.

Source: Journal of Scientific Computing; Dec2024, Vol. 101 Issue 3, p1-29, 29p

Monotone discretizations of levelset convex geometric PDEs.

Authors: Calder, Jeff Lee, Wonjun

Source: Numerische Mathematik; Dec2024, Vol. 156 Issue 6, p1987-2029, 43p

Subject Terms: BOUNDARY value problems, VISCOSITY solutions, DIRECTIONAL derivatives, CONVEX sets, POINT cloud, HAMILTON-Jacobi equations

Numerical approximations for fractional elliptic equations via the method of semigroups.

Authors: Cusimano, Nicole del Teso, Félix Gerardo-Giorda, Luca

Source: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN); 2020, Vol. 54 Issue 3, p751-774, 24p

Subject Terms: ELLIPTIC equations, SOBOLEV spaces, SINGULAR integrals, BOUNDARY value problems

AVOIDING DISCRETIZATION ISSUES FOR NONLINEAR EIGENVALUE PROBLEMS.

Source: SIAM Journal on Matrix Analysis & Applications; 2025, Vol. 46 Issue 1, p648-675, 28p

Subject Terms: NUMERICAL solutions for linear algebra, JACOBI operators, SINGULAR value decomposition, RAYLEIGH quotient, MATRIX pencils, SELFADJOINT operators, KRYLOV subspace

The Gross-Pitaevskii Equation and Eigenvector Nonlinearities: Numerical Methods and Algorithms.

Authors: Henning, Patrick Jarlebring, Elias

Source: SIAM Review; 2025, Vol. 67 Issue 2, p256-317, 62p

Subject Terms: GROSS-Pitaevskii equations, NONLINEAR Schrodinger equation, BOSE-Einstein condensation, ALGORITHMS, MATHEMATICAL optimization, QUANTUM theory, NUMERICAL analysis

Riemannian acceleration with preconditioning for symmetric eigenvalue problems.

Authors: Shao, Nian Chen, Wenbin

Source: Numerische Mathematik; Feb2025, Vol. 157 Issue 1, p307-354, 48p

Subject Terms: RIEMANNIAN manifolds, EIGENVALUES, BEHAVIORAL assessment, EXPONENTS, ANGLES

A Stabilization-Free Virtual Element Method for the Convection–Diffusion Eigenproblem.

Authors: Marcon, Francesca Mora, David

Source: Journal of Scientific Computing; Feb2025, Vol. 102 Issue 2, p1-33, 33p

Combinatorial and continuous Hodge theories

Authors: Dodziuk, Jozef

Source: Bull. Amer. Math. Soc. 80, no. 5 (1974), 1014-1016

Subject Terms: 39A05, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, 65N25, 53C65, 0102 computer and information sciences, Integral geometry, 0101 mathematics, General theory of difference equations, 01 natural sciences, Global Riemannian geometry, including pinching

File Description: application/xml; application/pdf

Access URL: https://www.ams.org/bull/1974-80-05/S0002-9904-1974-13615-3/S0002-9904-1974-13615-3.pdf
https://zbmath.org/3452782
https://doi.org/10.1090/s0002-9904-1974-13615-3
https://www.ams.org/bull/1974-80-05/S0002-9904-1974-13615-3/S0002-9904-1974-13615-3.pdf
https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-80/issue-5/Combinatorial-and-continuous-Hodge-theories/bams/1183535858.full
https://www.ams.org/journals/bull/1974-80-05/S0002-9904-1974-13615-3/
http://projecteuclid.org/euclid.bams/1183535858
https://projecteuclid.org/download/pdf_1/euclid.bams/1183535858
http://projecteuclid.org/euclid.bams/1183535858

Boundary-variation solution of eigenvalue problems for elliptic operators.

Authors: Bruno, Oscar Reitich, Fernando

Source: Journal of Fourier Analysis & Applications; Mar2001, Vol. 7 Issue 2, p169-187, 19p

Nontensorial generalised hermite spectral methods for PDEs with fractional Laplacian and Schrödinger operators.

Authors: Sheng, Changtao Ma, Suna Li, Huiyuan et al.

Source: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN); Sep/Oct2021, Vol. 55 Issue 5, p2141-2168, 28p

Subject Terms: SCHRODINGER operator, LAPLACIAN operator, HERMITE polynomials, FRACTIONAL integrals, SPARSE matrices