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This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM), for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
Peak performance metrics published by vendors often do not correspond to what can be achieved in practice. It is therefore of great interest to do extensive benchmarking on core applications and library routines. Since DGEMM is one of the…
Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…
Fully homomorphic encryption (FHE) enables direct computation on encrypted data, making it a crucial technology for privacy protection. However, FHE suffers from significant performance bottlenecks. In this context, GPU acceleration offers…
We study a family of $H^m$-conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of $2m$-th order partial differential equations in $\mathbb{R}^d$ for any $m,d…
The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. This method uses a finite element (FE) method to approximate the stresses and forces…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
In this work, we analyze a penalized variant of the {\phi}-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The {\phi}-FEM is a recently introduced unfitted finite element method based on a level-set description of…
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving…
Efficient and real time segmentation of color images has a variety of importance in many fields of computer vision such as image compression, medical imaging, mapping and autonomous navigation. Being one of the most computationally…
Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…
Cost of serving large language models (LLM) is high, but the expensive and scarce GPUs are poorly efficient when generating tokens sequentially, unless the batch of sequences is enlarged. However, the batch size is limited by some…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the…
We introduce Equivariant Neural Field Expectation Maximization (EFEM), a simple, effective, and robust geometric algorithm that can segment objects in 3D scenes without annotations or training on scenes. We achieve such unsupervised…
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…
Conventional mechanical design follows an iterative process in which initial concepts are refined through cycles of expert assessment and resource-intensive Finite Element Method (FEM) analysis to meet performance goals. While machine…