Related papers: Fireshape: a shape optimization toolbox for Firedr…
Nonlinear PDEs give rise to complex dynamics that are often difficult to analyze in state space due to their relatively large numbers of degrees of freedom, ill-conditioned operators, and changing spatial and parameter resolution…
FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The range of methods include molecular dynamics simulations to sample free…
We propose a framework for performing differentiable geometric modeling based on the Function Representation (FRep). The framework is built on top of modern libraries for performing automatic differentiation allowing us to obtain…
In this work, we introduce a new algorithm for N-to-M checkpointing in finite element simulations. This new algorithm allows efficient saving/loading of functions representing physical quantities associated with the mesh representing the…
Fireworks algorithm is a new type of intelligent optimization algorithm. Because of its fast convergence speed, easy implementation, explosiveness, diversity, simplicity and randomness, it has attracted more and more attention in many…
We consider the optimization problem for a shape cost functional $F(\Omega,f)$ which depends on a domain $\Omega$ varying in a suitable admissible class and on a "right-hand side" $f$. More precisely, the cost functional $F$ is given by an…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
The layer-upon-layer approach in additive manufacturing, open or closed cells in polymeric or metallic foams involve an intrinsic microstructure tailored to the underlying applications. Homogenization of such architectured materials creates…
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such \emph{macroelements} frequently enable the enforcement of mathematically desirable properties such as divergence-free…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…