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We study numerically the dispersion and dissipation properties of the plane wave virtual element method and the nonconforming Trefftz virtual element method for the Helmholtz problem. Whereas the former method is based on a conforming…
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB…
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
Fast and accurate resolution of electromagnetic problems via the \ac{BEM} is oftentimes challenged by conditioning issues occurring in three distinct regimes: (i) when the frequency decreases and the discretization density remains constant,…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the space and the reproducing kernel. If the volume of shells is…
The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green's function is replaced by a…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…
We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is…