4.7 Article

Automated translation and accelerated solving of differential equations on multiple GPU platforms

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Computer Science, Software Engineering

Construction of Rosenbrock-Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package

Gerd Steinebach

Summary: This paper introduces the efficiency of Rosenbrock-Wanner methods in solving systems of stiff ordinary differential equations and differential-algebraic equations of index-1. It shows that the disadvantage of updating the Jacobian matrix in every time step becomes less important with the use of automatic differentiation. The paper also computes a new set of coefficients for Rodas5 to reduce order reduction for certain problem classes.

BIT NUMERICAL MATHEMATICS (2023)

Article Mathematics, Applied

The art of solving a large number of non-stiff, low-dimensional ordinary differential equation systems on GPUs and CPUs

Daniel Nagy et al.

Summary: This paper discusses the main performance barriers and optimization techniques for solving a large number of independent ordinary differential equation systems on CPUs and GPUs.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2022)

Article Mathematics, Applied

Program package MPGOS: Challenges and solutions during the integration of a large number of independent ODE systems using GPUs

Ferenc Hegedus

Summary: This article discusses the challenges and efficient solutions for integrating a large number of independent ordinary differential equations on GPU architecture. Strategies include minimizing memory transactions and usage, handling asynchronous features, and overlapping GPU and CPU computations for increased efficiency.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

Article Biochemical Research Methods

SciPy 1.0: fundamental algorithms for scientific computing in Python

Pauli Virtanen et al.

NATURE METHODS (2020)

Article Computer Science, Theory & Methods

Effective Extensible Programming: Unleashing Julia on GPUs

Tim Besard et al.

IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS (2019)

Article Computer Science, Hardware & Architecture

ginSODA: massive parallel integration of stiff ODE systems on GPUs

Marco S. Nobile et al.

JOURNAL OF SUPERCOMPUTING (2019)

Article Computer Science, Interdisciplinary Applications

Rapid software prototyping for heterogeneous and distributed platforms

Tim Besard et al.

ADVANCES IN ENGINEERING SOFTWARE (2019)

Article Computer Science, Interdisciplinary Applications

SPFP: Speed without compromise-A mixed precision model for GPU accelerated molecular dynamics simulations

Scott Le Grand et al.

COMPUTER PHYSICS COMMUNICATIONS (2013)

Article Biochemical Research Methods

GPU accelerated biochemical network simulation

Yanxiang Zhou et al.

BIOINFORMATICS (2011)

Article Mathematics, Applied

Runge-Kutta pairs of order 5(4) satisfying only the first column simplifying assumption

Ch. Tsitouras

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2011)

Editorial Material Computer Science, Interdisciplinary Applications

OPENCL: A PARALLEL PROGRAMMING STANDARD FOR HETEROGENEOUS COMPUTING SYSTEMS

John E. Stone et al.

COMPUTING IN SCIENCE & ENGINEERING (2010)

Article Mathematics, Applied

Numerically optimal Runge-Kutta pairs with interpolants

J. H. Verner

NUMERICAL ALGORITHMS (2010)

Article Mathematical & Computational Biology

Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network

Clemens Kuehn et al.

BMC SYSTEMS BIOLOGY (2009)

Review Biology

A methodology for performing global uncertainty and sensitivity analysis in systems biology

Simeone Marino et al.

JOURNAL OF THEORETICAL BIOLOGY (2008)

Article Computer Science, Software Engineering

SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers

AC Hindmarsh et al.

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (2005)

Article Computer Science, Software Engineering

Singly diagonally implicit Runge-Kutta methods with an explicit first stage

A Kværno

BIT NUMERICAL MATHEMATICS (2004)

Article Mathematics, Applied

Weak second order conditions for stochastic Runge-Kutta methods

A Tocino et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2002)

Article Mathematics, Applied

Runge-Kutta methods for numerical solution of stochastic differential equations

A Tocino et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2002)

Article Chemistry, Physical

The chemical Langevin equation

DT Gillespie

JOURNAL OF CHEMICAL PHYSICS (2000)