A stable hybrid method for hyperbolic problems

A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

[1]  Jan Nordström,et al.  High Order Finite Difference Approximations of Electromagnetic Wave Propagation Close to Material Discontinuities , 2003, J. Sci. Comput..

[2]  Gunnar Ledfelt,et al.  Hybrid Time-Domain Methods and Wire Models for Computational Electromagnetics , 2001 .

[3]  Magnus Svärd,et al.  Artificial Dissipation for Strictly Stable Finite Volume Methods on Unstructured Meshes , 2004 .

[4]  Fredrik Edelvik,et al.  Explicit Hybrid Time Domain Solver for the Maxwell Equations in 3D , 2000, J. Sci. Comput..

[5]  M. Djordjevic,et al.  Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces , 2005, IEEE Transactions on Antennas and Propagation.

[6]  R. Mittra,et al.  A hybrid time-domain technique that combines the finite element, finite difference and method of moment techniques to solve complex electromagnetic problems , 2004, IEEE Transactions on Antennas and Propagation.

[7]  Magnus Svärd,et al.  Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids , 2004 .

[8]  B. Strand Summation by parts for finite difference approximations for d/dx , 1994 .

[9]  Bertil Gustafsson,et al.  The convergence rate for difference approximations to general mixed initial boundary value problems , 1981 .

[10]  U. Andersson,et al.  Time-Domain Methods for the Maxwell Equations , 2001 .

[11]  Fredrik Edelvik,et al.  A comparison of time‐domain hybrid solvers for complex scattering problems , 2002 .

[12]  Jan Nordström,et al.  High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates , 2001 .

[13]  Pierre Sagaut,et al.  A dynamic p-adaptive Discontinuous Galerkin method for viscous flow with shocks , 2005 .

[14]  Jan Nordström,et al.  Boundary and Interface Conditions for High-Order Finite-Difference Methods Applied to the Euler and Navier-Stokes Equations , 1999 .

[15]  D. Gottlieb,et al.  A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy , 1999 .

[16]  B. Gustafsson The convergence rate for difference approximations to mixed initial boundary value problems , 1975 .

[17]  Thomas Rylander,et al.  Stable FEM-FDTD hybrid method for Maxwell's equations , 2000 .

[18]  J. Nordström,et al.  Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients , 2004, Journal of Scientific Computing.

[19]  H. Kreiss,et al.  Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations , 1974 .

[20]  Bertil Gustafsson,et al.  On Error Bounds of Finite Difference Approximations to Partial Differential Equations—Temporal Behavior and Rate of Convergence , 2000, J. Sci. Comput..

[21]  Jan Nordström,et al.  Finite volume methods, unstructured meshes and strict stability for hyperbolic problems , 2003 .

[22]  D. Gottlieb,et al.  Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes , 1994 .

[23]  X. Ferrieres,et al.  Application of a hybrid finite difference/finite volume method to solve an automotive EMC problem , 2004, IEEE Transactions on Electromagnetic Compatibility.