GPU Implementation of Implicit Runge-Kutta Methods
نویسنده
چکیده
Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation of solutions of ordinary differential equations. Explicit RungeKutta methods are unsuitable for the solution of stiff equations as their region of stability is small. Stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is very small. This project aims in parallelizing implicit Runge-Kutta methods which are stable even for the stiff problems . The major disadvantage is that Implicit Runge-Kutta methods are more computationally expensive. We will show how to accelerate the execution of implicit Runge-Kutta methods using GPUs.
منابع مشابه
A GPU-Based Transient Stability Simulation Using Runge-Kutta Integration Algorithm
Graphics processing units (GPU) have been investigated to release the computational capability in various scientific applications. Recent research shows that prudential consideration needs to be given to take the advantages of GPUs while avoiding the deficiency. In this paper, the impact of GPU acceleration to implicit integrators and explicit integrators in transient stability is investigated....
متن کاملAn investigation of GPU-based stiff chemical kinetics integration methods
A fifth-order implicit Runge–Kutta method and two fourth-order exponential integration methods equipped with Krylov subspace approximations were implemented for the GPU and paired with the analytical chemical kinetic Jacobian software pyJac. The performance of each algorithm was evaluated by integrating thermochemical state data sampled from stochastic partially stirred reactor simulations and ...
متن کاملDesign and Implementation of Predictors for Additive Semi-Implicit Runge--Kutta Methods
Abstract. Space discretization of some time-dependent partial differential equations gives rise to stiff systems of ordinary differential equations. In this case, implicit methods should be used and therefore, in general, nonlinear systems must be solved. The solutions to these systems are approximated by iterative schemes and, in order to obtain an efficient code, good initializers should be u...
متن کاملGPU-Based Parallel Integration of Large Numbers of Independent ODE Systems
The task of integrating a large number of independent ODE systems arises in various scientific and engineering areas. For nonstiff systems, common explicit integration algorithms can be used on GPUs, where individual GPU threads concurrently integrate independent ODEs with different initial conditions or parameters. One example is the fifth-order adaptive Runge–Kutta– Cash–Karp (RKCK) algorithm...
متن کاملForward, Tangent Linear, and Adjoint Runge Kutta Methods in KPP–2.2 for Efficient Chemical Kinetic Simulations
The Kinetic PreProcessor (KPP) is a widely used software environment which generates Fortran90, Fortran77, Matlab, or C code for the simulation of chemical kinetic systems. High computational efficiency is attained by exploiting the sparsity pattern of the Jacobian and Hessian. In this paper we report on the implementation of two new families of stiff numerical integrators in the new version 2....
متن کامل