2 citations · 2 across the 9 of their papers we have counts for
10 papers
Conformal Spherical Splines for the Laplace--Beltrami Operator on Genus-Zero Surfaces: Construction, Algorithm, and Experiments
Shelvean Kapita
Every smooth closed Riemannian surface of genus zero is isometric to the unit sphere carrying a conformal metric, the round metric multiplied by a positive factor. This paper solve…
Bernstein Constraint Complexes for Multivariate Splines on Triangulated Surfaces
Shelvean Kapita
We introduce Bernstein constraint complexes, a representation of finite element differential complexes in which every triangle of a triangulation keeps its own Bernstein--Bézier co…
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…
A Bivariate Spline Solution to the Exterior Helmholtz Equation and Its Applications
Shelvean Kapita, Ming Jun Lai
We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study…
A Trefftz Discontinuous Galerkin Method for Time Harmonic Waves with Generalized Impedance Boundary Conditions
Shelvean Kapita, Peter Monk, Virginia Selgas
We show how a Trefftz Discontinuous Galerkin (TDG) method for the displacement form of the Helmholtz equation can be used to approximate problems having a generalized impedance bou…
A Plane Wave Discontinuous Galerkin Method with a Dirichlet-to-Neumann Boundary Condition for the Scattering Problem in Acoustics
Shelvean Kapita, Peter Monk
We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in . I…
Residual based adaptivity and PWDG methods for the Helmholtz equation
Shelvean Kapita, Peter Monk, T. Warburton
We present a study of two residual a posteriori error indicators for the Plane Wave Discontinuous Galerkin (PWDG) method for the Helmholtz equation. In particular we study the h-ve…