Related papers: Finite Element Theory for PHIMATS
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling…
Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations. We extended the code generation infrastructure in Firedrake…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This…
In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…
In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…
In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral…
Many numerical simulation tools have been developed and are on the market, but there is still a strong need for appropriate tools capable of simulating multi-field problems, especially in aeroacoustics. Therefore, openCFS provides an…
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations…
In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM)…