On the numerical solution of multi-dimensional parabolic problem by the additive splitting up method

Daoud, Daoud S.

doi:10.1016/j.amc.2003.12.093

Cited by 8 publications

(8 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. For the proof, see [21]. y The next algorithm is the second-order implicit splitting up algorithm given by Algorithm II.…”

Section: Algorithm I First-order Implicit Splitting Up Algorithmmentioning

confidence: 99%

Nonoverlapping domain decomposition and additive splitting up methods for multidimensional parabolic problem

Daoud¹

2005

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

The explicit implicit domain decomposition methods are noniterative types of methods for nonoverlapping domain decomposition but due to the use of the explicit step for the interface prediction, the methods suffer from inaccuracy of the usual explicit scheme. In this article a specific type of first-and second-order splitting up method, of additive type, for the dependent variables is initially considered to solve the twoor three-dimensional parabolic problem over nonoverlapping subdomains. We have also considered the parallel explicit splitting up algorithm to define (predict) the interface boundary conditions with respect to each spatial variable and for each nonoverlapping subdomains. The parallel second-order splitting up algorithm is then considered to solve the subproblems defined over each subdomain; the correction step will then be considered for the predicted interface nodal points using the most recent solution values over the subdomains. Finally several model problems will be considered to test the efficiency of the presented algorithm.

show abstract

“…Proof. For the proof, see [21]. y The next algorithm is the second-order implicit splitting up algorithm given by Algorithm II.…”

Section: Algorithm I First-order Implicit Splitting Up Algorithmmentioning

confidence: 99%

Nonoverlapping domain decomposition and additive splitting up methods for multidimensional parabolic problem

Daoud¹

2005

Numerical Methods Partial

Self Cite

View full text Add to dashboard Cite

show abstract

“…The concept of the algorithm proposed by Lu et al is similar to the classical fractional splitting but at each fractional step it contains an independent one-dimensional problem that is totally independent on the previous step, so that each fractional step can be assigned to different processors. For more about the algorithm and further applications to parabolic problem see [15,16,18,19]. In this article we present a new algorithm for splitting the multi-dimensional convection diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

On combination of first order Strang's splitting and additive splitting for the solution of multi-dimensional convection diffusion problem

Daoud¹

2007

International Journal of Computer Mathematics

Self Cite

View full text Add to dashboard Cite

In this article we present a new splitting approach for the numerical solution of the multi-dimensional convection diffusion equations. The method combines additive and multiplicative splitting. In particular the method combines first order Strang's splitting, multiplicative splitting defined for splitting the convection and diffusion equation, and additive splitting defined in accordance with the spatial variables. The method not only reduces the linear (or nonlinear) original problem into a series of one-dimensional and one physical operator linear problems, but also enables us to compute these onedimensional problems using parallel processors. The accuracy and stability of the new algorithm are investigated through the solution of different multi-dimensional convection diffusion model problems with scalar coefficients.

show abstract

“…Consider the following two-dimensional linear parabolic equation: Many efforts have been made to the development of accurate and stable methods for the numerical solution of (1) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Various high order methods [1-4, 6-9, 11-19] have been proposed.…”

Section: Introductionmentioning

confidence: 99%

“…Various high order methods [1-4, 6-9, 11-19] have been proposed. Among them, splitting strategies including alternating direction implicit (ADI) and locally one-dimensional (LOD) methods have been extensively explored for high order difference schemes [4,[6][7][8][9][11][12][13][14][15][16][17]. These methods are extremely efficient for solving multi-dimensional equations by converting multi-dimensional equations to successions of one-dimensional equations.…”

Section: Introductionmentioning

confidence: 99%

High order locally one-dimensional methods for solving two-dimensional parabolic equations

Chen

2018

Adv Differ Equ

View full text Add to dashboard Cite

Based on the locally one-dimensional strategy, we propose two high order finite difference schemes for solving two-dimensional linear parabolic equations. In the first method, fourth order approximation in space and (2, 2) Padé formula in time are considered. These lead to a fourth order finite difference scheme in both space and time. For the second method, we employ sixth order approximation in space and (3, 3) Padé formula in time. This yields a novel sixth order scheme in both space and time. The methods are proved to be unconditionally stable, and the Sheng-Suzuki barrier is successfully avoided. Numerical experiments are given to illustrate our conclusions as well as computational effectiveness.

show abstract

On the numerical solution of multi-dimensional parabolic problem by the additive splitting up method

Cited by 8 publications

References 7 publications

Nonoverlapping domain decomposition and additive splitting up methods for multidimensional parabolic problem

Nonoverlapping domain decomposition and additive splitting up methods for multidimensional parabolic problem

On combination of first order Strang's splitting and additive splitting for the solution of multi-dimensional convection diffusion problem

High order locally one-dimensional methods for solving two-dimensional parabolic equations

Contact Info

Product

Resources

About