Exact integration of polynomial-exponential products with application to wave-based numerical methods

DOI10.1002/cnm.1123zbMath1160.65309OpenAlexW1993081706MaRDI QIDQ3617462

Gwénaël Gabard

Publication date: 24 March 2009

Published in: Communications in Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cnm.1123

zbMATH Keywords

numerical examplesquadraturehighly oscillatory integralswave-based numerical methods

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

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Cites Work

• The partition of unity finite element method: basic theory and applications
• A comparison of some methods for the evaluation of highly oscillatory integrals
• Discontinuous Galerkin methods with plane waves for time-harmonic problems
• An improved partition of unity finite element model for diffraction problems
• Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
• Plane wave basis finite‐elements for wave scattering in three dimensions
• Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains
• New special wave boundary elements for short wave problems
• Special wave basis finite elements for very short wave refraction and scattering problems
• A numerical integration scheme for special quadrilateral finite elements for the Helmholtz equation
• Efficient quadrature of highly oscillatory integrals using derivatives
• Moment-free numerical integration of highly oscillatory functions
• Quadrature methods for multivariate highly oscillatory integrals using derivatives
• The discontinuous enrichment method

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