Related papers: Kernel Free Boundary Integral Method for 3D Stokes…
This paper introduces a second-order method for solving general elliptic partial differential equations (PDEs) on irregular domains using GPU acceleration, based on Ying's kernel-free boundary integral (KFBI) method. The method addresses…
This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the framework of Yee's scheme to eliminate null space and enable…
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…
A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
This paper describes a trapezoidal quadrature method for the discretization of singular and hypersingular boundary integral operators (BIOs) that arise in solving boundary value problems for elliptic partial differential equations. The…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
This paper introduces a new immersed boundary (IB) method for viscous incompressible flow, based on a Fourier spectral method for the fluid solver and on the nonuniform fast Fourier transform (NUFFT) algorithm for coupling the fluid with…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach,…
The purpose of this article is to introduce radial basis function, (RBFs), methods for solving null control problems for the Stokes system with few internal scalar controls and Dirichlet or Navier slip boundary conditions. To the best of…
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…
In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…