Related papers: A simple multigrid scheme for solving the Poisson …
The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamer discharges, since the Poisson solution appears as a source term of the unsteady nonlinear flow…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal…
We describe a simple and effective algorithm for solving Poisson's equation in the context of self-gravity within the DISPATCH astrophysical fluid framework. The algorithm leverages the fact that DISPATCH stores multiple time slices and…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network…
We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation which combines accuracy, computational efficiency and versatility. The solver, based on a mixed plane-wave / interpolating scaling function…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmholtz, Stokes and modified Stokes equations. The approach…
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the Poisson equations on manifolds from point clouds. In this…
Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
I present a motivation of several areas where the Multigrid techniques can be employed. I present typical areas where the multigrid solver might be employed. I give an introduction to smoothers and how one might choose a preconditionor as…
A novel coupled level-set lattice Boltzmann method on adaptive Cartesian grids for simulating liquid-gas multiphase flows is presented. The approach addresses the inherent challenges of accurately modeling multiphase systems characterized…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…