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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…
In recent years, high performance scientific computing on graphics processing units (GPUs) have gained widespread acceptance. These devices are designed to offer massively parallel threads for running code with general purpose. There are…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Accurate determination of the performance of parallel GPU code typically requires execution-time profiling on target hardware -- an increasingly prohibitive step due to limited access to high-end GPUs. This paper explores whether Large…
In general, there is a mismatch between a finite element model {(FEM)} of a structure and its real behaviour. In aeronautics, this mismatch must be small because {FEM}s are a fundamental part of the development of an aircraft and of…
Modern GPGPUs provide massive arithmetic throughput, yet many scientific kernels remain limited by memory bandwidth. In particular, repeatedly loading precomputed auxiliary data wastes abundant compute resources while stressing the memory…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…
Finite element schemes based on discontinuous Galerkin methods possess features amenable to massively parallel computing accelerated with general purpose graphics processing units (GPUs). However, the computational performance of such…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…
We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
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…
Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
The multi-level hp-refinement scheme is a powerful extension of the finite element method that allows local mesh adaptation without the trouble of constraining hanging nodes. This is achieved through hierarchical high-order overlay meshes,…
Adjacent GEMM problems that differ by a single 128-element step in N can show 30% different throughput on the same GPU. This pervasive performance ruggedness - invisible to roofline analysis and peak-FLOPs intuition, yet dominant for every…
Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…