Related papers: Mat2Boundary: Treating User-Defined Boundary Condi…
In compressed sensing, the sensing matrix is assumed perfectly known. However, there exists perturbation in the sensing matrix in reality due to sensor offsets or noise disturbance. Directions-of-arrival (DoA) estimation with off-grid…
A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the…
The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like…
Accurately solving time-dependent partial differential equations (PDEs) with neural networks remains challenging due to long-time error accumulation and the difficulty of enforcing general boundary conditions. We introduce TENG-BC, a…
Distributed Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in high-performance computing and deep learning applications. The major performance bottleneck in distributed SpMM lies in substantial communication overhead,…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
Program verification is a resource-hungry task. This paper looks at the problem of parallelizing SMT-based automated program verification, specifically bounded model-checking, so that it can be distributed and executed on a cluster of…
A Waveguide Port Boundary Condition (WPBC) based on the restriction of the approximation space is presented in the context of Finite Element Analysis. As well as reducing the computational domain in the same manner as the traditional WPBC,…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in $H(\mathrm{div})$. The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc…
In this paper, we present the Semantic Boundary Conditioned Backbone (SBCB) framework, a simple yet effective training framework that is model-agnostic and boosts segmentation performance, especially around the boundaries. Motivated by the…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Sparse matrix-vector multiplication (SpMV) is the core operation in many common network and graph analytics, but poor performance of the SpMV kernel handicaps these applications. This work quantifies the effect of matrix structure on SpMV…
Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with…
The sparse matrix-vector product (SpMV) is a fundamental operation in many scientific applications from various fields. The High Performance Computing (HPC) community has therefore continuously invested a lot of effort to provide an…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…