Operator-splitting Method for High-dimensional Parabolic Equation via Finite Element Method
نویسندگان
چکیده
This work introduces a new operator-splitting method for solving the two-dimensional (2D) and three-dimensional (3D) parabolic equations. The aim is to reduce the computational complexity without loss of accuracy. Firstly, we split the 2D and 3D parabolic equations into a sequence of one-dimensional (1D) parabolic equations respectively, then we solve each 1D parabolic equation by using finite element method. In comparison with standard finite element method, the present method can save much CPU time. Furthermore, the stability analysis and error estimates for the proposed method are derived. Finally, numerical results of the 2D and 3D parabolic equations are presented to support our theoretical analysis.
منابع مشابه
Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems
Keywords: Operator-splitting method Finite element method Parabolic equations High-dimensional problems a b s t r a c t An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algori...
متن کاملA new positive definite semi-discrete mixed finite element solution for parabolic equations
In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations. Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...
متن کاملOperator splitting methods for pricing American options under stochastic volatility
We consider the numerical pricing of American options under Heston’s stochastic volatility model. The price is given by a linear complementarity problem with a two-dimensional parabolic partial differential operator. We propose operator splitting methods for performing time stepping after a finite difference space discretization. The idea is to decouple the treatment of the early exercise const...
متن کاملExplicit Implicit Non Overlapping Domain Decomposition Method with Splitting up method for Multi Dimensional Parabolic Problem
The explicit implicit domain decomposition methods are a non iterative types of methods for non overlapping domain decomposition. In comparison with the classical Schwarz algorithm for parabolic problem the former methods are computationally and communicationally more efficient for each time step but due to the use of the explicit step for the interface prediction the methods suffer from the ac...
متن کاملOperator Splitting for Three-Phase Flow in Heterogeneous Porous Media
We describe an operator splitting technique based on physics rather than on dimension for the numerical solution of a nonlinear system of partial differential equations which models three-phase flow through heterogeneous porous media. The model for three-phase flow considered in this work takes into account capillary forces, general relations for the relative permeability functions and variable...
متن کامل