相关论文: Multithreaded Filtering Preconditioner for Diffusi…
We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…
In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid…
To amortize cost, cloud vendors providing DNN acceleration as a service to end-users employ consolidation and virtualization to share the underlying resources among multiple DNN service requests. This paper makes a case for a "preemptible"…
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…
Diffusion models have achieved great success in synthesizing high-quality images. However, generating high-resolution images with diffusion models is still challenging due to the enormous computational costs, resulting in a prohibitive…
Diffusion models demonstrate outstanding performance in image generation, but their multi-step inference mechanism requires immense computational cost. Previous works accelerate inference by leveraging layer or token cache techniques to…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
Due to the wide separation of time scales in geophysical fluid dynamics, semi-implicit time integrators are commonly used in operational atmospheric forecast models. They guarantee the stable treatment of fast (acoustic and gravity) waves,…
A Multigrid Full Approximation Storage algorithm for solving Deep Residual Networks is developed to enable neural network parallelized layer-wise training and concurrent computational kernel execution on GPUs. This work demonstrates a 10.2x…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
Diffusion Transformers (DiT) are powerful generative models but remain computationally intensive due to their iterative structure and deep transformer stacks. To alleviate this inefficiency, we propose \textbf{FastCache}, a…
As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid…
The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are…
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…
The whole computer hardware industry embraced multicores. For these machines, the extreme optimisation of sequential algorithms is no longer sufficient to squeeze the real machine power, which can be only exploited via thread-level…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
In this article we present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution of certain control-constrained, quadratic distributed optimal control problems. Using a piecewise constant…