Related papers: Lebesgue integration. Detailed proofs to be formal…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
This article develops a unified and intrinsic framework for the theory of Sobolev spaces on vector bundles over Riemannian manifolds. The analytical core of our approach is an explicit higher-order geometric integration by parts formula,…
In a recent paper, Belle and Levesque proposed a framework for a type of program called belief programs, a probabilistic extension of GOLOG programs where every action and sensing result could be noisy and every test condition refers to the…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…
We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define…
L^p spaces of mappings taking values in arbitrary metric spaces, which we call nonlinear Lebesgue spaces, play an important role in several fields of mathematics. For instance, membership in these spaces is typically required for transport…
A major determinant of the quality of software systems is the quality of their requirements, which should be both understandable and precise. Most requirements are written in natural language, good for understandability but lacking in…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified…
Measure Theory and Integration is exposed with the clear aim to help beginning learners to perfectly master its essence. In opposition of a delivery of the contents in an academic and vertical course, the knowledge is broken into exercises…
Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…
This article provides formal definitions characterizing well-formed composition of components in order to guarantee their safe deployment and execution. Our work focuses on the structural aspects of component composition; it puts together…
In this article, using an exemplar-based approach, we investigate the inpainting problem, introducing a new mathematical functional, whose minimization determines the quality of the reconstructions. The new functional expression takes into…
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…
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 focus on the finite element method computations with higher-order C1 continuity basis functions that preserve the partition of unity. We show that the rows of the system of linear equations can be combined, and the test functions can be…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
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…