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We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to…
Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs.…
Improvements in computer systems have historically relied on two well-known observations: Moore's law and Dennard's scaling. Today, both these observations are ending, forcing computer users, researchers, and practitioners to abandon the…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a…
Structural optimization has been a crucial component in computational materials research, and structure predictions have relied heavily on this technique in particular. In this study, we introduce a novel method that enhances the efficiency…
We introduce an efficient video segmentation system for resource-limited edge devices leveraging heterogeneous compute. Specifically, we design network models by searching across multiple dimensions of specifications for the neural…
In recent years, topology optimization (TO) has gained widespread attention as a powerful structural design method. However, its application remains challenging due to the deep expertise and extensive development effort required.…
In this paper, we present a NURBS-enhanced finite element method that integrates the NURBS-based boundary representation of a geometric domain into a standard finite element framework for hexahedral meshes. We decompose an open, bounded,…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
Privacy-preserving machine learning (PPML) is an emerging topic to handle secure machine learning inference over sensitive data in untrusted environments. Fully homomorphic encryption (FHE) enables computation directly on encrypted data on…
GPU-based heterogeneous architectures are now commonly used in HPC clusters. Due to their architectural simplicity specialized for data-level parallelism, GPUs can offer much higher computational throughput and memory bandwidth than CPUs in…
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the…
The request for high-quality solutions continually grows in a world where more and more tasks are executed through computers. This also counts for fields such as engineering, computer graphics, etc., which use meshes to solve their…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…
The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…