Related papers: Solving DWF Dirac Equation Using Multi-splitting P…
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…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are both…
Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both…
We present details of our implementation of the Wuppertal adaptive algebraic multigrid code DD-$\alpha$AMG on SIMD architectures, with particular emphasis on the Intel Xeon Phi processor (KNC) used in QPACE 2. As a smoother, the algorithm…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
The multigroup neutron transport criticality calculations using modern supercomputers have been widely employed in a nuclear reactor analysis for studying whether or not a system is self-sustaining. However, the design and development of…
In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…
As deep learning continues to advance and is applied to increasingly complex scenarios, the demand for concurrent deployment of multiple neural network models has arisen. This demand, commonly referred to as multi-tenant computing, is…
The performance and efficiency of distributed training of Deep Neural Networks highly depend on the performance of gradient averaging among all participating nodes, which is bounded by the communication between nodes. There are two major…
We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…
The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite quadratic subproblem by an interior point approach. For larger cutting model sizes the limiting…
We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps…
An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space…
Efficient deployment of Deep Neural Networks (DNNs), such as Large Language Models (LLMs), on tensor accelerators is essential for maximizing computational efficiency in modern AI systems. However, achieving this is challenging due to the…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…
Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision…