Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains

DOI10.1137/110834950zbMath1269.65130OpenAlexW2038068268MaRDI QIDQ2904829

Jie Shen, Hai-jun Yu

Publication date: 23 August 2012

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

Full work available at URL: https://doi.org/10.1137/110834950

zbMATH Keywords

unbounded domainssparse gridspectral methodhigher-dimensional problemselectronic Schrödinger equationmapped Chebyshev functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (17)

Fourier spectral method on sparse grids for computing ground state of many-particle fractional Schrödinger equations ⋮ Efficient spectral sparse grid approximations for solving multi-dimensional forward backward sdes ⋮ Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients, I. The One-Dimensional Case ⋮ A new collocation method using near-minimal Chebyshev quadrature nodes on a square ⋮ A Fast Cartesian Grid-Based Integral Equation Method for Unbounded Interface Problems with Non-Homogeneous Source Terms ⋮ Sparse grid discontinuous Galerkin methods for the Vlasov-Maxwell system ⋮ The Adaptive Spectral Koopman Method for Dynamical Systems ⋮ A parallel sparse grid construction algorithm based on the shared memory architecture and its application to flash calculations ⋮ Efficient high order method for differential equations in unbounded domains using generalized coordinate transformation ⋮ Efficient spectral methods for quasi-equilibrium closure approximations of symmetric problems on unit circle and sphere ⋮ Efficient Mapping of High Order Basis Sets for Unbounded Domains ⋮ Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units ⋮ The Hermite pseudospectral method for the two-dimensional Schrödinger equation with nonseparable potentials ⋮ Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains ⋮ Efficient Spectral-Element Methods for the Electronic Schrödinger Equation ⋮ Sparse Grid Central Discontinuous Galerkin Method for Linear Hyperbolic Systems in High Dimensions ⋮ Exact solutions to a nonlinear partial differential equation: the Product-of-Curvatures Poisson \((u_{x x} u_{y y} = 1)\)

This page was built for publication: Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Equations II. Unbounded Domains