Related papers: A compiler for variational forms
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
Matrix-free finite element implementations for large applications provide an attractive alternative to standard sparse matrix data formats due to the significantly reduced memory consumption. Here, we show that they are also competitive…
Finite Element Exterior Calculus (FEEC) was developed by Arnold, Falk, Winther and others over the last decade to exploit the observation that mixed variational problems can be posed on a Hilbert complex, and Galerkin-type mixed methods can…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis…
We propose and analyze an adaptive finite element method for a phase-field model of dynamic brittle fracture. The model couples a second-order hyperbolic equation for elastodynamics with the Ambrosio-Tortorelli regularization of the…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
The photonic platform holds great promise for quantum computing. Nevertheless, the intrinsic probabilistic characteristics of its native fusion operations introduces substantial randomness into the computing process, posing significant…
Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…
This paper presents an educational code written using FEniCS, based on the level set method, to perform compliance minimization in structural optimization. We use the concept of distributed shape derivative to compute a descent direction…
Core spanners are a class of document spanners that capture the core functionality of IBM's AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be seen as a logic for core…