A Fast Method for Solving the Helmholtz Equation Based on Wave Splitting
2009 (English)Licentiate thesis, monograph (Other academic)
In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one--way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one--way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one--way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one--way wave equations are solved with GO with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge-Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is just O(ω1/p) for a p-th order Runge-Kutta method. This has been confirmed by numerical experiments.
Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , viii, 70 p.
Trita-CSC-A, ISSN 1653-5723 ; 2009:11
Helmholtz equation, high fequency waves
IdentifiersURN: urn:nbn:se:kth:diva-10517ISBN: 978-91-7415-370-5OAI: oai:DiVA.org:kth-10517DiVA: diva2:218666
2009-06-12, D41, KTH, Lindstedtsvägen 5, Stockholm, 13:15 (English)
Larsson, Elisabeth, Ass. Prof.
Runborg, Olof, Prof.