Parallelizing a fourth-order Runge-Kutta method

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U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology , Gaithersburg, MD
Runge-Kutta form
Other titlesParallelizing a fourth order Runge Kutta method
StatementHai C. Tang.
SeriesNISTIR -- 6031
ContributionsNational Institute of Standards and Technology (U.S.)
The Physical Object
Pagination26 p.
ID Numbers
Open LibraryOL17121238M

Get this from a library. Parallelizing a fourth-order Runge-Kutta method. [Hai C Tang; National Institute of Standards and Technology (U.S.)]. Through research for the method of serial classic fourth-order Runge-Kutta and based on the method, we construct Parallel fourth-order Runge-Kutta method in.

In this paper, we develop, analyze, and evaluate a parallel algorithm for diagonally explicit Runge-Kutta method of order four (DERK4) for solving systems of differential equations.

The time extrapolation is carried out by a fourth-order Runge–Kutta method. An algorithm similar to the one described in this paper—for the 2-D Cartesian case—is described in Carcione & Wang ().

Boundary conditionsCited by: Using a four-core CPU, it is natural to think about fourth-order RIDC built with forward Euler, or eighth-order RIDC constructed with second-order Runge–Kutta. Numerical tests on an N-body simulation show that RIDC methods can be significantly faster than popular Runge–Kutta methods such as the classical fourth-order Runge–Kutta scheme Cited by: As many as 22 million mesh points have been used in these simulations.

Time advancement Parallelizing a fourth-order Runge-Kutta method book by a fourth order Runge-Kutta algorithm.

Description Parallelizing a fourth-order Runge-Kutta method FB2

From the point of view of a programmer implementing the algorithm on a parallel computer, the most significant aspect of the algorithm is that the differencing schemes are all non-local. Evaluation of compact Author: Parviz Moin, Bendiks J. Boersma, Jonathan B.

Freund, Arthur G. Kravchenko, Charles D. Pierce. The particle part makes use of the fact that in the desired equilibrium state the pressure along magnetic field lines is constant and determines a new distribution p for fixed B →: From each grid point a magnetic field line is started and traced by solving an ordinary differential equation with an 8-stage Runge-Kutta : R.

Dohmen, U. Schwerin. Posted by Hamid R. Arabnia, AM. Fourth order IMEX Runge-Kutta method I am looking for the Butcher tableau of a fourth order accurate Runge-Kutta method with IMEX splitting. I have been reading the ''classical'' paper on the subject by Ascher, Ruuth and Spiteri as well.

ode_rk4, a MATLAB code which interactively applies a fourth order Runge-Kutta method to estimate the solution of an ordinary differential equation y'=f(x,y), over the interval [a,b], with initial condition y(a)=ya, using n steps.

() Development and Application of an Exponential Method for Integrating Stiff Systems Based on the Classical Runge–Kutta Method.

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Differential Equations() Decay chain differential equations: Solutions through matrix by: Q&A for scientists using computers to solve scientific problems. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. Abstract. The author presents an approach to find stochastic bounds for Markov chains with the use of Intel Xeon Phi coprocessor. A known algorithm is adapted to study the potential of the MIC architecture in algorithms needing a lot of Cited by: 1.

To solve the LIF neuron model differential equation, a fourth-order Runge–Kutta method was implemented.

This differential equation is processed offline in event-driven methods [10] (to build up the neural characterization lookup tables) and online in time-driven methods [22].

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions.

The method was applicable on a mesh-free set of data nodes. Up: Refereed Proceeedings: N. Alhazmi, Y. Ghazi, C. Farhat, P. Avery and R. Tezaur, "Parametric Studies of Aerodynamic Properties of Wings Using Various Forms of Machine Learning", Third International Conference on Computer Applications and Information Security (ICCAIS ), Riyadh, Saudi Arabia, March () C.

White, D. Ushizima and C. The output from the low pass filter shown above "builds up and settles" quickly: A fourth order band pass filter with band to requires more samples for the center frequency to build up and settle: Some notes on db +3 db is twice the power -3 db is half the power +10 db is ten times the power db is one tenth the power +30 db.

Also in [], a class of nonlinearly stable high order Runge-Kutta time discretization methods is developed. Termed TVD time discretizations, these Runge-Kutta methods have become very popular and have been used in many schemes.

See, e.g.

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[65] for a review of such methods. Analysis of ENO schemes was given in Harten et al. [77]. A new method for the solution of pentadiagonal systems of linear equations is presented.

The method is a generalization of ordinary odd-even elimination used for tridiagonal systems. Using n processors, an n X n Cited by: 2. 08/08/18 - In this paper we present the Python framework pySDC for solving collocation problems with spectral deferred correction methods (SD. You need an interface to the function: The user then provides an implementation to the function to pass to the integration method and may provide values: The pre written integration method example, has the numeric code, yet does not know the function (yet): The files are: test_aquad.c aquad.h aquad.

This banner text can have markup. web; books; video; audio; software; images; Toggle navigation. Full text of "Studying Turbulence Using Numerical Simulation Databases - X Proceedings of the Summer Program" See other formats.

Parallelizing a poorly optimized algorithm is a waste of time. Optimizing a badly conceived algorithm is a waste of time. Applying a well conceived algorithm to an inappropriate numerical method is a waste of time.

Failure to understand these things has led to a colossal waste of computing and human resources. Computation with Red, Blue and Yellow.

Implicit Runge-Kutta Methods with Explicit Internal Stages. NASA Astrophysics Data System (ADS) Skvortsov, L.

The main computational costs of implicit Runge-Kutta methods are caused by solving a system of algebraic equations at every step. By introducing explicit stages, it is possible to increase the stage (or pseudo-stage) order of the. Numerical Recipes in Fortran The Art of Parallel Scientific Computing, Volume 2 of Fortran Numerical Recipes, Second Edition, first published this book is intended as a text and reference book, for reading purposes only.

allocatable array) is in routine rkdumb on page An example of Method 1 with SAVE is in routine pwtset. The Boundary Element Method (BEM) has become established as an effective tool for the solutions of problems in engineering science.

The salient features of the BEM have been well documented in the open literature and therefore will not be elaborated here. I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem.

Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide Cited by: The FCT method (Boris and Book ) focused on eliminating unphysical oscillations.

It is a hybrid scheme that mixes first-order and second-order accuracy in a nonlinear manner. The MUSCL schemes of van Leer () are a more direct generalization of Godunov’s method in which the initial states of the underlying Riemann problem are modified.

Get this from a library. Parallel computing: software technology, algorithms, architectures & applications: proceedings of the International Conference ParCo, Dresden, Germany, September [G Joubert;]. ANNA UNIVERSITY, CHENNAI – UNIVERSITY DEPARTMENTS. R- (INFORMATION TECHNOLOGY) I-VIII SEMESTERS CURRICULA AND SYLLABUS.

SEMESTER I. SEMESTER II. COURSE COD.% LiteralHTML: % LiteralHTML: Research and Publications that make use of PETSc % LiteralHTML: % LiteralHTML: Nano-simulations % LiteralHTML: @article{RuppPIS, author = {Rupp, Karl and Weinbub, Josef and J\"{u}ngel, Ansgar and Grasser, Tibor}, title = {Pipelined Iterative Solvers with Kernel Fusion .The salient features of statistical method are given in Section (PG).

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