Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity

DOI10.1137/S1064827597330613zbMath0981.65132MaRDI QIDQ4942061

No author found.

Publication date: 20 March 2000

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplesdomain decompositionLaplace equationPetrov-Galerkin methodsparse approximate inversesecond-order elliptic problemwavelet preconditioningwavelet adaptive refinement

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for wavelets (65T60) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Complexity and performance of numerical algorithms (65Y20)

Related Items (21)

Blind wavelet compression of the solution of a nonlinear PDE with singular forcing term within optimal order cost: stability of restricted approximation to small errors ⋮ New wavelet preconditioner for solving boundary integral equations over nonsmooth boundaries ⋮ Hat interpolation wavelet-based multi-scale Galerkin method for thin-walled box beam analysis ⋮ A Daubechies wavelet-based method for elastic problems ⋮ Wavelet bases in $\mathbf{H}( \mathrm{div})$ and $\mathbf{H}(\mathbf{curl})$ ⋮ An operator splitting algorithm for Tikhonov-regularized topology optimization ⋮ Stabilized wavelet approximations of the Stokes problem ⋮ Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals ⋮ AN OPERATOR SPLITTING PRECONDITIONER FOR MATRICES ARISING FROM A WAVELET BOUNDARY ELEMENT METHOD FOR THE HELMHOLTZ EQUATION ⋮ A new fast method of solving the high dimensional elliptic eigenvalue problem ⋮ Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations ⋮ An adaptive multilevel wavelet collocation method for elliptic problems ⋮ The Mortar Method in the Wavelet Context ⋮ No-slip and free-slip divergence-free wavelets for the simulation of incompressible viscous flows ⋮ Iterative algorithms for multiscale state estimation. I: Concepts ⋮ A numerical strategy to discretize and solve the Poisson equation on dynamically adapted multiresolution grids for time-dependent streamer discharge simulations ⋮ Study on spline wavelet finite-element method in multi-scale analysis for foundation ⋮ Wavelet Galerkin Methods for Higher Order Partial Differential Equations ⋮ Divergence-Free Wavelet Projection Method for Incompressible Viscous Flow on the Square ⋮ Preconditioning techniques for large linear systems: A survey ⋮ Adaptive wavelet methods for elliptic operator equations: Convergence rates

This page was built for publication: Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity