Related papers: A Matrix-Free Galerkin Multigrid Solver and Failur…

The Digital Image processing applications like medical imaging, satellite imaging, Biometric trait images etc., rely on multipliers to improve the quality of image. However, existing multiplication techniques introduce errors in the output…

A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…

This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…

An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method…

We develop a discontinuous Galerkin (DG) framework for automatically constructing adaptive basis sets for electronic structure calculations. By allowing basis functions to be discontinuous across element interfaces, our approach supports…

The IEEE 754-2008 standard recommends the correct rounding of some elementary functions. This requires to solve the Table Maker's Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such…

General matrix/matrix multiplication (GEMM) is crucial for scientific computing and machine learning. However, the increased scale of the computing platforms raises concerns about hardware and software reliability. In this poster, we…

An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a…

In this work, we present a framework for the matrix-free solution to a monolithic quasi-static phase-field fracture model with geometric multigrid methods. Using a standard matrix based approach within the Finite Element Method requires…

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…

Recent works demonstrate the advantages of hardware rasterization for 3D Gaussian Splatting (3DGS) in forward-pass rendering through fast GPU-optimized graphics and fixed memory footprint. However, extending these benefits to backward-pass…

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is…

GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…

High-frequency ground motion simulations pose a grand challenge in computational seismology. Two main factors drive this challenge. First, to account for higher frequencies, we have to extend our numerical models, e.g., by considering…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many…

The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…

Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free…