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Numerical Solution of the Helmholtz Equation in 2D and 3D Using a High-Order Nyström Discretization

✍ Scribed by Lawrence F. Canino; John J. Ottusch; Mark A. Stalzer; John L. Visher; Stephen M. Wandzura

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
383 KB
Volume
146
Category
Article
ISSN
0021-9991

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✦ Synopsis

We show how to solve time-harmonic scattering problems by means of a highorder Nyström discretization of the boundary integral equations of wave scattering in 2D and 3D. The novel aspect of our new method is its use of local corrections to the discretized kernel in the vicinity of the kernel singularity. Enhanced by local corrections, the new algorithm has the simplicity and speed advantages of the traditional Nyström method, but also enjoys the advantages of high-order convergence for controlling solution error. We explain the practical details of implementing a scattering code based on a high-order Nyström discretization and demonstrate by numerical example that a scattering code based on this algorithm can achieve high-order convergence to the correct answer. We also demonstrate its performance advantages over a high-order Galerkin code.

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✍ A. E. Merzon; F.-O. Speck; T. J. Villalba-Vega 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 312 KB 👁 1 views

We extend previous results for the Neumann boundary value problem to the case of boundary data from the space H -1 2 +e (C), 0<e< 1 2 , where C = \*X is the boundary of a two-dimensional cone X with angle b<p. We prove that for these boundary conditions the solution of the Helmholtz equation in X ex