Related papers: Comparative study of different quadrature methods …
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…
A quadrature method for second-order, curved triangular elements in the Boundary Element Method (BEM) is presented, based on a polar coordinate transformation, combined with elementary geometric operations. The numerical performance of the…
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,…
We present new and efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for wave propagation modelling. These quadrature rules allow for a more efficient implementation of the mass-lumped…
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…
Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over…
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
We investigate the numerical implementation of functionally graded properties in the context of the finite element method. The macroscopic variation of elastic properties inherent to functionally graded materials (FGMs) is introduced at the…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…
The evaluation of clustering algorithms can involve running them on a variety of benchmark problems, and comparing their outputs to the reference, ground-truth groupings provided by experts. Unfortunately, many research papers and graduate…
AI-assisted coding has rapidly reshaped software practice and research workflows, yet today's models still struggle to produce correct code for complex 3D geometric vision. If models could reliably write such code, the research of our…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necessarily conforming to the boundaries/interfaces of the…