Related papers: FIAT: improving performance and accuracy for high-…
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…
The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
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 work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability…
We introduce new method of optimization for finding free parameters of affine iterated function systems (IFS), which are used for fractal approximation. We provide the comparison of effectiveness of fractal and quadratic types of…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
The emergence of data-driven computational materials science offers unprecedented opportunities to explore complex material landscapes, complementing experimental research with the discovery of novel compounds. To enable these developments,…
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…
The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and…
This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions are…
Retrieving relevant evidence from visually rich documents such as textbooks, technical reports, and manuals is challenging due to long context, complex layouts, and weak lexical overlap between user questions and supporting pages. We…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We introduce Tangent Attention Fine-Tuning (TAFT), a method for fine-tuning linearized transformers obtained by computing a First-order Taylor Expansion around a pre-trained initialization. We show that the Jacobian-Vector Product resulting…
The rise of code pre-trained models has significantly enhanced various coding tasks, such as code completion, and tools like GitHub Copilot. However, the substantial size of these models, especially large models, poses a significant…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…