Related papers: Towards a Machine-Learned Poisson Solver for Low-T…
Poisson's equation is the canonical elliptic partial differential equation. While there exist fast Poisson solvers for finite difference and finite element methods, fast Poisson solvers for spectral methods have remained elusive. Here, we…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design. Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage. The…
In this paper, the application of quantum computing (QC) in solving gate insulator Poisson equation is studied, through QC simulator and hardware in IBM. Various gate insulator stacks with and without fixed charges are studied. It is found…
A solver for the Poisson equation for 1D, 2D and 3D regular grids is presented. The solver applies the convolution theorem in order to efficiently solve the Poisson equation in spectral space over a rectangular computational domain.…
In this paper we prove discrete to continuum convergence rates for Poisson Learning, a graph-based semi-supervised learning algorithm that is based on solving the graph Poisson equation with a source term consisting of a linear combination…
Although having achieved the promising results on shape and color recovery through self-supervision, the multi-layer perceptrons-based methods usually suffer from heavy computational cost on learning the deep implicit surface…
Separated flow transition is a very popular phenomenon in gas turbines, especially low-pressure turbines (LPT). Low-fidelity simulations are often used for gas turbine design. However, they are unable to predict separated flow transition…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
This study proposes a high-efficient machine learning (ML) projection method using forward-generated data for incompressible Navier-Stokes equations. A Poisson neural network (Poisson-NN) embedded method and a wavelet transform…
A 3-dimensional GPU Poisson solver is developed for all possible combinations of free and periodic boundary conditions (BCs) along the three directions. It is benchmarked for various grid sizes and different BCs and a significant…
Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
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…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…
Since self-gravity is crucial in the structure formation of the universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the…
We introduce Neural Poisson Surface Reconstruction (nPSR), an architecture for shape reconstruction that addresses the challenge of recovering 3D shapes from points. Traditional deep neural networks face challenges with common 3D shape…