38 citations · 179 across the 22 of their papers we have counts for
5 papers · 1 filter
The Helmholtz Dirichlet and Neumann problems on piecewise smooth open curves
Johan Helsing, Shidong Jiang
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners…
Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries
Johan Helsing, Shidong Jiang
A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The…
Variants of an explicit kernel-split panel-based Nyström discretization scheme for Helmholtz boundary value problems
Johan Helsing, Anders Holst
The incorporation of analytical kernel information is exploited in the construction of Nyström discretization schemes for integral equations modeling planar Helmholtz boundary valu…
An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces
Johan Helsing, Anders Karlsson
A high-order accurate, explicit kernel-split, panel-based, Fourier-Nyström discretization scheme is developed for integral equations associated with the Helmholtz equation in axial…
A higher-order singularity subtraction technique for the discretization of singular integral operators on curved surfaces
Johan Helsing
This note is about promoting singularity subtraction as a helpful tool in the discretization of singular integral operators on curved surfaces. Singular and nearly singular kernels…