An Advanced Numerical Approach for Wave Propagation Problems in Isotropic and Aniso-Tropic Composite and Functionally Graded Materials. Application to High Frequency Pulse Propagation in the Hopkinson
Technical Report,01 Aug 2016,31 Jul 2019
Texas Tech University System Lubbock United States
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A new high-order accurate numerical approach has been developed for wave propagation in isotropic and anisotropic composite and functionally graded materials. It does not use any weak formulation for the derivation of the semi-discrete system of equations. The coefficients of the semi-discrete system of equations are directly derived from the minimization of the order of the local truncation error and provide the optimal order of accuracy. The new approach is much more accurate than other known numerical techniques e.g., finite elements, isogeometric elements, finite volume method and other . A new highorder accurate procedure has been also developed for the Dirichlet and Neumann boundary conditions that includes the time and spatial derivatives of the boundary conditions. This provides the same high order of accuracy of the stencils for internal and boundary points. The new approach has been first tested on rectangular domains and has shown a significant decrease in the computation time by a factor of 10 - 1000 and more compared to that for the high-order isogeometric elements at the same accuracy. The application of the new high-order accurate approach to complicated irregular domains shows a much bigger decrease in the computational costs.
- Radiofrequency Wave Propagation
- Laminates and Composite Materials
- Numerical Mathematics