Parallelized Simulation of a Finite Element Method in Many Integrated Core Architecture

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Moonho Tak ◽  
Taehyo Park
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Linear Algebra ◽  
Message Passing ◽  
Message Passing Interface ◽  
Domain Decomposition Method ◽  
Xeon Phi ◽  
Parallel Libraries ◽  
Many Integrated Core ◽  
Element Method

We investigate a domain decomposition method (DDM) of finite element method (FEM) using Intel's many integrated core (MIC) architecture in order to determine the most effective MIC usage. For this, recently introduced high-scalable parallel method of DDM is first introduced with a detailed procedure. Then, the Intel's Xeon Phi MIC architecture is presented to understand how to apply the parallel algorithm into a multicore architecture. The parallel simulation using the Xeon Phi MIC has an advantage that traditional parallel libraries such as the message passing interface (MPI) and the open multiprocessing (OpenMP) can be used without any additional libraries. We demonstrate the DDM using popular libraries for solving linear algebra such as the linear algebra package (LAPACK) or the basic linear algebra subprograms (BLAS). Moreover, both MPI and OpenMP are used for parallel resolutions of the DDM. Finally, numerical parallel efficiencies are validated by a two-dimensional numerical example.

Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

2019 ◽  
Vol 38 (5) ◽  
pp. 1507-1520 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Koji Fujiwara ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Computing ◽  
Domain Decomposition ◽  
Parallel Computation ◽  
Domain Decomposition Method ◽  
Space Time ◽  
Content Type ◽  
Parallel Performance ◽  
Element Method

Purpose This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment. Design/methodology/approach First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors. Findings The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost. Originality/value This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

Stabilized numerical method for solving the Oseen type problem with a singularity

2018 ◽  
Author(s):  
А.В. Рукавишников
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Krylov Subspace ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Algebraic Equations ◽  
Type Problem ◽  
Curvilinear Boundary ◽  
Linear Algebraic Equations ◽  
Element Method

На основе метода декомпозиции области построен стабилизационный неконформный метод конечных элементов для решения задачи типа Озеена. Для конвективно доминирующих течений с разрывным коэффициентом вязкости определена шкала оптимального выбора стабилизирующего параметра. Результаты численных экспериментов согласуются с теоретической оценкой сходимости. Purpose. To construct modified approximation approach using the finite element method and to perform numerical analysis for a two dimensional problem on the flow of a viscous inhomogeneous fluids — the Oseen type problem, that is obtained by sampling in time and linearizing the incompressible Navier—Stokes equations. To consider the convection dominated flow case. Methodology. Based on the domain decomposition method with a smooth curvilinear boundary between subdomains, a stabilization nonconformal finite element method is constructed that satisfies the inf-sup-stability condition. To solve the resulting system of linear algebraic equations, an iterative process is considered that uses the decomposition of the vector in the Krylov subspace with minimal inviscidity, with a block preconditioning of the matrix. Findings. The results of the numerical experiments demonstrate the robustness of the considered method for different (even small) discontinuous values of viscosity. The differences between finite element and exact solutions for the velocity field and pressure in the norms of the grid spaces decrease as

Mixed Hybrid Finite Element Method for a Variational Inequality with a Quasi-linear Operator

2009 ◽  
Vol 9 (4) ◽  
pp. 354-367 ◽  
Author(s):  
A. Lapin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Inequality ◽  
Domain Decomposition Method ◽  
Linear Differential Operator ◽  
Element Approximation ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Mixed Hybrid Finite Element ◽  
Element Method

Abstract A mixed hybrid finite element method has been applied to a variational inequality with a potential second-order quasi-linear differential operator. The Lagrange multiplier method for a dual problem has been used to construct this finite element scheme. The existence and uniqueness of a solution for the resulting finite- dimensional problem has been proved, the solution iterative methods are discussed. The non-overlapping domain decomposition method combined with the mixed hybrid finite element approximation is analyzed.

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