Related papers: Iterative Krylov Methods for Acoustic Problems on …
This paper gives an analysis and an evaluation of linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetics with double precision. Knowing the performance of these operations, iterative Krylov methods are…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
In this paper, the authors propose an analysis of the frequency response function in a car compartment, subject to some fluctuating pressure distribution along the open cavity of the sun-roof at the top of a car. Coupling of a computational…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy…
In this paper, we aim to introduce a new perspective when comparing highly parallelized algorithms on GPU: the energy consumption of the GPU. We give an analysis of the performance of linear algebra operations, including addition of…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Krylov methods are a key way of solving large sparse linear systems of equations, but suffer from poor strong scalabilty on distributed memory machines. This is due to high synchronization costs from large numbers of collective…
Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical…
Since numbers in the computer are represented with a fixed number of bits, loss of accuracy during calculation is unavoidable. At high precision where more bits (e.g. 64) are allocated to each number, round-off errors are typically small.…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…
Context. Numerical solutions to transfer problems of polarized radiation in solar and stellar atmospheres commonly rely on stationary iterative methods, which often perform poorly when applied to large problems. In recent times, stationary…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
Solving large, sparse linear systems is a fundamental workload in scientific computing and engineering simulations, often dominating runtime and energy consumption in high-performance computing (HPC) applications. In this work, we explore…
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and…
With the steady advance of high performance computing systems featuring smaller and smaller hardware components, the systems and algorithms used for numerical simulations increasingly contend with disruptions caused by hardware failures and…
This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel…
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace…