Publication

KUL and EPFL cooperation on numerical integration of Sommerfeld integrals

Juan Ramon Mosig, Ruzica Golubovic, Athanasios Polymeridis
2012
Conference Papers

Abstract

This paper reports the result of the cooperation between KUL and EPFL on the numerical integration of Sommerfeld integrals (SI). Each institution is well-known for developing specific techniques suited for the evaluation of SI: double-exponential quadrature rules to take the tail of the integral into account (EPFL) and an asymptotic extraction technique to remove the singularities (KUL). The combination of these two techniques results in a very promising algorithm, allowing to perform the integration along the real axis only. Several examples illustrate the algorithm efficiency.

Official source

https://infoscience.epfl.ch/entities/publication/bbe6e575-0615-4034-8d52-80319c8ed72c

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Juan Ramon Mosig, Ruzica Golubovic, Athanasios Polymeridis
2012
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/bbe6e575-0615-4034-8d52-80319c8ed72c

About this result

Related concepts (19)

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Verlet integration

Verlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

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