Related papers: Finite element computation of absorbing boundary c…
We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…
In density-based topology optimization, design variables associated to the boundaries of the design domain require unique treatment to negate boundary effects arising from the filtering technique. An effective approach to deal with…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
In the framework of the optimal wave energy absorption, we solve theoretically and numerically a parametric shape optimization problem to find the optimal distribution of absorbing material in the reflexive one defined by a characteristic…
We present a ray-based finite element method (ray-FEM) by learning basis adaptive to the underlying high-frequency Helmholtz equation in smooth media. Based on the geometric optics ansatz of the wave field, we learn local dominant ray…
We present a novel immersed boundary method that implements acoustic perturbation theory to model an acoustically levitated droplet. Instead of resolving sound waves numerically, our hybrid method solves acoustic scattering…
In this paper we consider wave viscoelastic equation with dynamic boundary condition in a bounded domain, we establish a general decay result of energy by exploiting the frequency domain method which consists in combining a contradiction…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
The geometries of surface wave modes are determined by the highly nontrivial interplay of capillarity and wetting effects at the boundaries of their domain. Aside from idealised scenarios, this commonly leads to unknown boundary conditions,…
For some anisotropic wave models, the PML (perfectly matched layer) method of open boundaries can become polynomially or exponentially unstable in time. In this work we present a new method of open boundaries, the phase space filter, which…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where…
Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…
It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary condition can be used to solve the Helmholtz equation in unbounded domains. In this work, applying such DtN boundary condition and using the finite element method,…
In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in…