Related papers: A robust and non-singular formulation of the bound…
Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…
The computational cost of the boundary-condition-enforced immersed boundary method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of Lagrangian points, $N$, increases. This is due to the time-consuming calculation of the…
The boundary knot method (BKM) [1] is a meshless boundary-type radial basis function (RBF) collocation scheme, where the nonsingular general solution is used instead of fundamental solution to evaluate the homogeneous solution, while the…
This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…
Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) [Dong, Lai, Li, Mathematics of Computation,2021]. The main appeal of this…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve…