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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-10517 |
| Date | January 2009 |
| Creators | Popovic, Jelena |
| Publisher | KTH, Numerisk analys, NA, Stockholm : KTH |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, monograph, info:eu-repo/semantics/masterThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | Trita-CSC-A, 1653-5723 ; 2009:11 |
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