Related papers: Solving Poisson's Equation on the Microsoft HoloLe…
We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an…
We introduce a PDE-based node-to-element contact formulation as an alternative to classical, purely geometrical formulations. It is challenging to devise solutions to nonsmooth contact problem with continuous gap using finite element…
{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite…
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…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
In this paper, we study the biharmonic equation with Dirichlet boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-order problem into a system of two Poison equations and one…
The Poisson-Fermi model is an extension of the classical Poisson-Boltzmann model to include the steric and correlation effects of ions and water treated as nonuniform spheres in aqueous solutions. Poisson-Boltzmann electrostatic…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
Holographic displays hold the promise of providing authentic depth cues, resulting in enhanced immersive visual experiences for near-eye applications. However, current holographic displays are hindered by speckle noise, which limits…
Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
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…
We derive a mixed integer nonlinear programming formulation for the problem of finding a convex polygon with a given number of vertices that is small (diameter at most one) and has maximum perimeter. The formulation is based on a geometric…
We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel…
Foveated imaging provides a better tradeoff between situational awareness (field of view) and resolution and is critical in long-wavelength infrared regimes because of the size, weight, power, and cost of thermal sensors. We demonstrate…
We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a…
This paper introduces a novel approach for learning polynomial representations of physical objects. Given a point cloud data set associated with a physical object, we solve a one-class classification problem to bound the data points by a…
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…