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Foundation Models (FMs) have become essential components in modern software systems, excelling in tasks such as pattern recognition and unstructured data processing. However, their capabilities are complemented by the precision,…
Modern and future high precision pointing space missions face increasingly high challenges related to the widespread use of large flexible structures. The development of new modeling tools which are able to account for the multidisciplinary…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized…
Like other engineering disciplines, software engineering should also have principles to guide the construction of sustainable computer applications. Tangible properties include a) unlimited scalability, b) maximal reproducibility, and c)…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
Energy and pollution are urging problems of the 21th century. By gradually changing the actual power grid system, smart grid may evolve into different systems by means of size, elements and strategies, but its fundamental requirements and…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
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…
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…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
Ecological systems can be seen as networks of interactions between individual, species, or habitat patches. A key feature of many ecological networks is their organization into modules, which are subsets of elements that are more connected…
We present a "multipatch" infrastructure for numerical simulation of fluid problems in which sub-regions require different gridscales, different grid geometries, different physical equations, or different reference frames. Its key element…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
In this tutorial paper, we will firstly review some basic simulation concepts and then introduce the parallel and distributed simulation techniques in view of some new challenges of today and tomorrow. More in particular, in the last years…
This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…