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The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial discretization of the resulting time-domain boundary integral…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
An overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyzed by the authors ({\tt J. Comput. Phys., {\bf 403}, 109052,…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment.…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…
The famous scientist Hermann von Helmholtz was born 200 years ago. Many complex physical wave phenomena in engineering can effectively be described using one or a set of equations named after him: the Helmholtz equation. Although this has…
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…
The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
In a previous article [J. Comp. Phys. $\mathbf{357}$ (2018) 282-304], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…
Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…
The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling…
The Boundary Element Method (BEM) is implemented using piecewise linear elements to solve the two-dimensional Dirichlet problem for Laplace's equation posed on a disk. A benefit of the BEM as opposed to many other numerical solution…