Reciprocal-Log Approximation and Planar PDE Solvers

DOI10.1137/20M1369555zbMath1482.65220arXiv2010.01807MaRDI QIDQ5164016

Yuji Nakatsukasa, Lloyd N. Threfethen

Publication date: 9 November 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.01807

zbMATH Keywords

rational approximationlightning solverreciprocal-log approximation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Approximation by other special function classes (41A30)

Related Items (6)

Automatic model order reduction for systems with frequency-dependent material properties ⋮ AAA-least squares rational approximation and solution of Laplace problems ⋮ Numerical analytic continuation ⋮ Confluent Vandermonde with Arnoldi ⋮ Lightning Stokes Solver ⋮ Rectangular eigenvalue problems

Uses Software

• DLMF
• AAA

Cites Work

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• Asymptotic development of the solution of Dirichlet's problem at analytic corners
• Development of the mapping function at an analytic corner
• An extension of the `1/9'-problem
• The convergence of Padé approximants to functions with branch points
• Fejér-Walsh points for rational functions and their use in the ADI iterative method
• Exponential node clustering at singularities for rational approximation, quadrature, and PDEs
• Talbot quadratures and rational approximations
• Chebyshev rational approximations to \(e^{-x}\) in \([0,+\infty)\) and applications to heat-conduction problems
• The Exponentially Convergent Trapezoidal Rule
• Visual Complex Functions
• Parabolic and hyperbolic contours for computing the Bromwich integral
• Vandermonde with Arnoldi
• New Laplace and Helmholtz solvers
• Solving Laplace Problems with Corner Singularities via Rational Functions
• Discrete Inverse Problems
• The AAA Algorithm for Rational Approximation
• Lightning Stokes Solver
• A Padé-based algorithm for overcoming the Gibbs phenomenon

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