相关论文: Automated formulation and resolution of limit anal…

Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their…

A generic framework for the solution of PDE-constrained optimisation problems based on the FEniCS system is presented. Its main features are an intuitive mathematical interface, a high degree of automation, and an efficient implementation…

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.…

We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…

An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associated code can solve both linear and non-linear problems, and…

The success of several constraint-based modeling languages such as OPL, ZINC, or COMET, appeals for better software engineering practices, particularly in the testing phase. This paper introduces a testing framework enabling automated test…

ConArg is a Constraint Programming-based tool that can be used to model and solve different problems related to Abstract Argumentation Frameworks (AFs). To implement this tool we have used JaCoP, a Java library that provides the user with a…

The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…

Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only…

As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…

We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…

In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the…

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis…

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…

Solving partial differential equations with the finite element method leads to large linear systems of equations that must be solved. When these systems have a natural block structure due to multiple field variables, using iterative solvers…

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…

We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…