Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems. (English) Zbl 1085.65099
Summary: The fifth in a series, the high-order spectral finite-volume, or spectral volume (SV) method for unstructured grids is extended to three dimensions. Limitations of conventional structured and unstructured methods are first reviewed. The spectral finite-volume method for generalized conservation laws is then described. It is shown that if all grid cells are partitioned into structured sub-cells in a similar manner, the discretizations become universal, and are reduced to the same weighted sum of unknowns involving just a few simple adds and multiplies. Important aspects of the data structure and its effects on communication and the optimum use of cache memory are discussed.
Previously defined one-parameter partitions of the SV in 2D are extended to multiple parameters and then used to construct 3D partitions. Numerical solutions of plane electromagnetic waves incident on perfectly conducting circular cylinders and spheres are presented and compared with the exact solution to demonstrate the capability of the method. Excellent agreement has been found. Computation timings show that the new method is more efficient than conventional structured and unstructured methods.
[For part IV see Z. J. Wang, L. Zhang, and Y. Liu, ibid. 194, No. 2, 716–741 (2004; Zbl 1039.65072).]
Previously defined one-parameter partitions of the SV in 2D are extended to multiple parameters and then used to construct 3D partitions. Numerical solutions of plane electromagnetic waves incident on perfectly conducting circular cylinders and spheres are presented and compared with the exact solution to demonstrate the capability of the method. Excellent agreement has been found. Computation timings show that the new method is more efficient than conventional structured and unstructured methods.
[For part IV see Z. J. Wang, L. Zhang, and Y. Liu, ibid. 194, No. 2, 716–741 (2004; Zbl 1039.65072).]
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 35Q40 | PDEs in connection with quantum mechanics |
| 78A25 | Electromagnetic theory (general) |
Keywords:
numerical examples; Maxwell equations; spectral finite-volume method; electromagnetic wavesSoftware:
MathematicaReferences:
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