5 papers
Odd behaviour of even geometries: an explanation for superconvergent geometric consistency errors
Hanne Hardering, Simon Praetorius, Gentian Zavalani
Piecewise polynomial surface approximations used in surface finite element methods often seem to behave better than their standard approximation properties suggest if their polynom…
Cubature from rational approximation
Gentian Zavalani
We present a numerical construction of cubature rules for area integrals of analytic functions over planar domains with rectifiable Jordan boundary. The starting point is the Cauch…
A High-Order Fast Direct Solver for Surface PDEs on Triangles
Gentian Zavalani
We develop a triangular formulation of the hierarchical Poincaré-Steklov (HPS) method for elliptic partial differential equations on surfaces, allowing high-order discretizations o…
Fast high-order spectral solvers for PDEs on triangulated surfaces with applications to deforming surfaces
Gentian Zavalani
In this paper, we extend the classical quadrilateral based hierarchical Poincaré-Steklov (HPS) framework to triangulated geometries. Traditionally, the HPS method takes as input an…
High-order numerical integration on regular embedded surfaces
Gentian Zavalani, Michael Hecht
We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting sq…