Fast Spectrally-Accurate Solution of Variable-Coefficient Elliptic Problems

DOI10.2307/2160763zbMath0812.65099OpenAlexW4248823176MaRDI QIDQ4318307

John Strain

Publication date: 14 May 1995

Full work available at URL: https://doi.org/10.2307/2160763

zbMATH Keywords

numerical examplespreconditioningfast Fourier transformiterative methodperiodic coefficientsmultigrid methodsGreen functioncrystal growthspectral methodsuniform ellipticity

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Statistical mechanics of crystals (82D25) Iterative numerical methods for linear systems (65F10)

Related Items (5)

An efficient and robust spectral solver for nonseparable elliptic equations ⋮ Locally-corrected spectral methods and overdetermined elliptic systems ⋮ Curvature-Driven Molecular Flow on Membrane Surface ⋮ A comparison of splittings and integral equation solvers for a nonseparable elliptic equation ⋮ Applications of semi-implicit Fourier-spectral method to phase field equations

Uses Software

• RODAS

Cites Work

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• Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning
• Application of volume integrals to the solution of partial differential equations
• Iterative methods with spectral preconditioning for elliptic equations
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Rapid solution of integral equations of scattering theory in two dimensions
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• On the Numerical Solution of Helmholtz's Equation by the Capacitance Matrix Method
• Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
• Use of Fast Direct Methods for the Efficient Numerical Solution of Nonseparable Elliptic Equations

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