期刊
FINITE DIFFERENCE METHODS, THEORY AND APPLICATIONS
卷 9045, 期 -, 页码 50-61出版社
SPRINGER-VERLAG BERLIN
DOI: 10.1007/978-3-319-20239-6_5
关键词
Trefftz functions; Finite difference schemes; Boundary difference schemes; Maxwell equations; Wave propagation; Effective medium theory; Discontinuous galerkin methods; Nonreflecting boundary conditions; Metamaterials
In problems of mathematical physics, Trefftz approximations by definition involve functions that satisfy the differential equation of the problem. The power and versatility of such approximations is illustrated with an overview of a number of application areas: (i) finite difference Trefftz schemes of arbitrarily high order; (ii) boundary difference Trefftz methods analogous to boundary integral equations but completely singularity-free; (iii) Discontinuous Galerkin (DG) Trefftz methods for Maxwell's electrodynamics; (iv) numerical and analytical nonreflecting Trefftz boundary conditions; (v) non-asymptotic homogenization of electromagnetic and photonic metamaterials.
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