Related papers: A parallel method for solving Laplace equations wi…
In this paper the isogeometric Nystr\"om method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only…
The interior Dirichlet boundary value problem for the diffusion equation in non-homogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in (Fresneda-Portillo, 2019) different…
We present methods for locally solving the Dynamic Programming Equations (DPE) and the Hamilton Jacobi Bellman (HJB) PDE that arise in the infinite horizon optimal control problem. The method for solving the DPE is the discrete time version…
A method for analytical computation of the double surface integrals for all layer potential kernels associated with the Laplace Green's function, in the Galerkin boundary element method (BEM) in $\mathbb{R}^3$ using piecewise constant flat…
We describe a parallel algorithm for solving the time-independent 3d Schrodinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…
The purpose of this article is to provide a solution to the $m$-fold Laplace equation in the half space $R_+^d$ under certain Dirichlet conditions. The solutions we present are a series of $m$ boundary layer potentials. We give explicit…
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 simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dimensions. An expansion in curvilinear coordinates leads us to…
The demagnetization field in micromagnetism is given as the gradient of a potential which solves a partial differential equation (PDE) posed in R^d. In its most general form, this PDE is supplied with continuity condition on the boundary of…
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary…
A new numerical method is developed to approximate the solution of Laplace's equation in the exterior of the sphere with a strongly nonlinear boundary value of oblique type. A functional analysis attempt to solve this type of boundary…
This study introduces a recursive method for computing asymptotic solutions of the Laplace equation in corner domains with the homogeneous Dirichlet boundary condition on one side and the Robin boundary condition with a power-law…
In a major advance and simplification of this field, we show that A Local Resolution of the Problem of Time - also viewable as A Local Theory of Background Independence - can at the classical level be described solely by of Lie's…
A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the…
Several important problems in partial differential equations can be formulated as integral equations. Often the integral operator defines the solution of an elliptic problem with specified jump conditions at an interface. In principle the…
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…
In this thesis, we develop path integral localization methods that are familiar from topological field theory: the integral over the infinite dimensional integration domain depends only on local data around some finite dimensional…