4 papers
Adaptive local representations for Helmholtz Trefftz discontinuous Galerkin methods
Shelvean Kapita
We study the selection and stable realization of local approximation spaces in Trefftz discontinuous Galerkin discretizations of the Helmholtz equation. A scaled Cauchy-trace inner…
Efficient Bernstein Quasi-Trefftz Discretization for Heterogeneous High-Frequency Helmholtz Problems
Shelvean Kapita
We develop an efficient Bernstein quasi-Trefftz discretization for heterogeneous high-frequency Helmholtz problems on unstructured triangular meshes. The method first imposes…
The PWDG-UWVF Equivalence Revisited
Shelvean Kapita
The ultra-weak variational formulation (UWVF) is known to be the Trefftz discontinuous Galerkin scheme obtained from the standard PWDG flux family by setting \(α=β=δ=1/2\). We give…
Direction-Adaptive Plane-Wave Discontinuous Galerkin Methods for the Helmholtz Equation
Shelvean Kapita
We consider plane-wave discontinuous Galerkin (PWDG) approximations of the Helmholtz equation with adaptive local propagation directions. The directions are chosen by minimizing a…