Hierarchical Domain Decomposition Method Research Articles

Parallel wave sound analysis based on hierarchical domain decomposition method

Parallel wave sound analysis based on hierarchical domain decomposition method

Parallel full-wave electromagnetic field analysis based on hierarchical domain decomposition method

Parallel full-wave electromagnetic field analysis based on hierarchical domain decomposition method

A Relation of Preconditioners in Domain Decomposition Method for Magnetostatic Problems

An iterative domain decomposition method is proposed for numerical analysis of three-dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the preconditioned conjugate gradient (PCG) procedure and the hierarchical domain decomposition method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann–Neumann (NN) preconditioner. Numerical results showed that the method was only effective for problems with a small number of subdomains. In this paper, we show its improvement with the balancing domain decomposition diagonal scaling (BDD-DIAG) preconditioner and show the asymptotic equivalence between BDD-DIAG and the simplified diagonal scaling (diag) preconditioner, which is derived from the following numerical evidences.

Parallel Simulation of Aerodynamic Instabilities in Transonic Axial Compressor Rotor

Although significant advances have been made in simulations of rotating stall and surge with single passage or part-annulus passages models, quite little work has been devoted to three-dimensional unsteady full-annulus simulations of the aerodynamic instabilities. In this Paper, a hierarchical domain decomposition method coupled with an artificial interface method is proposed and applied to the full-annulus simulations of three-dimensional aerodynamic instabilities in NASA rotor 35 at low flow rates. The compressor–throttle valve model and compressor–plenum chamber model are adopted to consider the effects of pipe network system on the compressor. The parallel results fit both the serial results and experimental data well, and the parallel efficiency is around 84% with 432 processor cores. With compressor–throttle valve model, rotating stall is observed in that the unsteady performance path converges to a fixed point, and the rotating speed, number, and size of stall cells vary slightly from the stall inception to the developed stall. With the compressor–plenum chamber model, mild surge is observed in that the unsteady performance path converges to a limit cycle oscillation, and low-frequency and large-amplitude axisymmetric oscillations propagate periodically along the axial direction. The occurrence of rotating stall or surge is consistent with the well-established laws of parameter .

Hierarchical Domain Decomposition Method for Devices including Moving Bodies

Hierarchical Domain Decomposition Method for Devices including Moving Bodies

部分領域を直接法で解く場合のインターフェイス問題の反復法について

An iterative domain decomposition method is proposed for numerical analysis of 3-Dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the Preconditioned Conjugate Gradient (PCG) procedure and the Hierarchical Domain Decomposition Method (HDDM). Our previously employed preconditioner was the Neumann-Neumann preconditioner. Numerical results showed that the method was only effective for smaller problems. In this paper, we consider its improvement with a balancing domain decomposition preconditioner (BDD-DIAG). Specially, we consider the direct subdomain solver in this short presentation.

Improvement of Convergence in Time-Harmonic Eddy Current Analysis with Hierarchical Domain Decomposition Method

Improvement of Convergence in Time-Harmonic Eddy Current Analysis with Hierarchical Domain Decomposition Method

154 大規模解析のための多階層領域分割法ソルバの開発

154 大規模解析のための多階層領域分割法ソルバの開発

HIERARCHICAL DOMAIN DECOMPOSITION WITH PARALLEL MESH REFINEMENT FOR BILLIONS-OF-DOF SCALE FINITE ELEMENT ANALYSES

This paper describes a parallel fast generation method of large-scale meshes for a hierarchical domain decomposition method implemented in the open source parallel finite element software ADVENTURE. Since large-scale meshes need to be generated in order to perform various analyses in Japan's Petaflops Supercomputer, nicknamed the "K computer", a mesh refinement function and a communication table generation function without communication are newly developed and implemented for the hierarchical domain decomposition tool named ADVENTURE_Metis. The developed new version is named ADVENTURE_Metis Ver.2. Since a generation cost of a communication table for sending and receiving data among computational nodes becomes so expensive for the refined large-scale mesh, the present authors have newly developed a parallel algorithm such that the communication tables of vertices, edges and faces are updated each other during mesh refinement after the initial communication tables of vertices, edges and faces are generated for an initial mesh. As a result, the generation of a refined mesh model over billions degrees of freedom (DOFs) from an initial medium-size mesh model of about a million DOFs can be performed in a parallel computer in a short time.

A 3D radiative transfer framework

Multi-level non-local thermodynamic equilibrium (NLTE) radiation transfer calculations have become standard throughout the stellar atmospheres community and are applied to all types of stars as well as dynamical systems such as novae and supernovae. Even today spherically symmetric 1D calculations with full physics are computationally intensive. We show that full NLTE calculations can be done with fully 3 dimensional (3D) radiative transfer. With modern computational techniques and current massive parallel computational resources, full detailed solution of the multi-level NLTE problem coupled to the solution of the radiative transfer scattering problem can be solved without sacrificing the micro physics description. We extend the use of a rate operator developed to solve the coupled NLTE problem in spherically symmetric 1D systems. In order to spread memory among processors we have implemented the NLTE/3D module with a hierarchical domain decomposition method that distributes the NLTE levels, radiative rates, and rate operator data over a group of processes so that each process only holds the data for a fraction of the voxels. Each process in a group holds all the relevant data to participate in the solution of the 3DRT problem so that the 3DRT solution is parallelized within a domain decomposition group. We solve a spherically symmetric system in 3D spherical coordinates in order to directly compare our well-tested 1D code to the 3D case. We compare three levels of tests: a) a simple H+He test calculation, b) H+He+CNO+Mg, c) H+He+Fe. The last test is computationally large and shows that realistic astrophysical problems are solvable now, but they do require significant computational resources. With presently available computational resources it is possible to solve the full 3D multi-level problem with the same detailed micro-physics as included in 1D modeling.

静磁場問題の領域分割解析におけるBDD前処理の適用

An iterative domain decomposition method is proposed for numerical analysis of 3-Dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the Preconditioned Conjugate Gradient (PCG) procedure and the Hierarchical Domain Decomposition Method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann-Neumann preconditioner. Numerical results showed that the method was only effective for smaller problems. In this paper, we consider its improvement with the Balancing Domain Decomposition (BDD) preconditioner.

Study on Parallel Computing Method of 3-D Dynamic Analysis of Large-Scale Structure

In order to solve 3-D dynamic problem for large-scale structure, based on HDDM (Hierarchical Domain Decomposition Method) method, 3-D dynamic finite element parallel computing method of large-scale structure is studied. In this paper, BDD method and Newmark-β average acceleration method in time integration is used. Based on ADVENTRUE program, the corresponding linear implicit transient dynamic parallel program which is based on the MPI parallel environment and can be used in shared memory and distributed memory parallel computer is prepared. Several pre-conditioners are contrasted using some examples, and the results show that BDD preconditioner or BDD-DIAG preconditioner can be used in 3-D dynamic analysis for large-scale structure.

Study on Parallel Computing Method of 3-D Dynamic Analysis of Large-Scale Structure

In order to solve 3-D dynamic problem for large-scale structure, based on HDDM (Hierarchical Domain Decomposition Method) method, 3-D dynamic finite element parallel computing method of large-scale structure is studied. In this paper, BDD method and Newmark-β average acceleration method in time integration is used. Based on ADVENTRUE program, the corresponding linear implicit transient dynamic parallel program which is based on the MPI parallel environment and can be used in shared memory and distributed memory parallel computer is prepared. Several pre-conditioners are contrasted using some examples, and the results show that BDD preconditioner or BDD-DIAG preconditioner can be used in 3-D dynamic analysis for large-scale structure.

Nonlinear multiscale modeling approach to characterize elastoplastic behavior of CNT/polymer nanocomposites considering the interphase and interfacial imperfection

A hierarchical multiscale modeling approach to characterize the elastic and plastic behavior of carbon nanotube (CNT)-reinforced polymer nanocomposites is proposed via molecular dynamics simulations and a continuum nonlinear micromechanics based on the secant moduli method. Even though the importance of the densified interphase zone formed between the CNT and polymer matrix has been demonstrated by many related studies for elastic properties, studies on how to identify the behavior and contribution of the interfacial condition and interphase zone in the overall elastoplastic behavior of nanocomposites is still an open issue. Different from conventional micromechanics approaches that homogenize overall elastoplastic behavior of heterogeneous structures from known behaviors of its constituent phases, the present study focuses on the identification of local elastoplastic behavior of the interphase region from the known elastoplastic behavior of nanocomposites through a hierarchical domain decomposition method. Firstly, the overall elastoplastic behavior of the CNT-reinforced nanocomposites is obtained from molecular dynamics (MD) simulations which are based on an ab initio force field. Due to a weak van der Waals interaction between the pristine CNT and the matrix polymer, the elastoplastic behavior of the nanocomposites clearly shows a weakened interface condition, while the matrix molecular structure in the vicinity of the CNT confirms the existence of the interphase zone. In upper level analysis, an effective matrix concept is adopted, and its elastoplastic behavior is inversely identified by equating the MD simulation result to a two-phase nonlinear micromechanics model that can consider imperfect interfacial condition. Then, the effective matrix domain is again decomposed into the interphase and pure matrix polymer regions in lower level analysis, and the elastoplastic behavior of the interphase is again identified through the same method. Using the constitutive relation of the interphase obtained from the proposed multiscale model, the overall elastoplastic behavior of the nanocomposites is obtained and compared with some available experimental results and an additional MD simulation result to validate the applicability and physical rigorousness of the proposed nonlinear multiscale approach.

F101 BDD前処理の統一的構築方法についての一考察(F1.低炭素社会向けシミュレーション技術,フォーラム)

An iterative domain decomposition method is applied to numerical analysis of 3-Dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the Preconditioned Conjugate Gradient (PCG) procedure and the Hierarchical Domain Decomposition Method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann-Neumann preconditioner. Numerical results showed that the method was only effective for smaller problems. In this paper, we consider its improvement with the Balancing Domain Decomposition (BDD) preconditioner. Also, we discuss a unified approach for the construction of BDD preconditioners in various applications including elastic problems, heat transfer problems and incompressible viscous flow problems besides magnetostatic problems.

An efficient modified hierarchical domain decomposition for two-dimensional magnetotelluric forward modelling

We use 2-D magnetotelluric (MT) problems as a feasibility study to demonstrate that 3-D MT problems can be solved with a direct solver, even on a standard single processor PC. The scheme used is a hierarchical domain decomposition (HDD) method in which a global computational domain is uniformly split into many smaller non-overlapping subdomains. To make it more efficient, two modifications are made to the standard HDD method. Instead of three levels as in the standard HDD method, we classify the unknowns into four classes: the interiors, the horizontal interfaces, the vertical interfaces and the intersections. Four sets of smaller systems of equations are successively solved with a direct method (an LU factorization). The separation significantly reduces the large memory requirements of a direct solver. It also reduces the CPU time to almost half that of the standard HDD method although it is still slower than the conventional finite difference (FD) method. To further enhance the speed of the code, a red-black ordering is applied to solve the horizontal and vertical interface reduced systems. Numerical experiments on a 2-D MT problem of a given size running on a single processor machine shows that CPU time and memory used are almost constant for any resistivity models, frequencies and modes. This is a clear advantage of our algorithm and is of particular importance if the method is applied to 3-D problems. We show that our new method results in reductions in both memory usage and CPU time for large enough domains when compared to the standard FD and HDD schemes. In addition, we also introduce a ‘memory minimization map’, a graphical tool we can use instead of trial-and-error to pre-select the optimal size of subdomains, which yield the best performance in both CPU time and memory even running on a serial machine.

Incomplete Balancing Domain Decomposition for Large scale 3-D non-stationary incompressible flow problems

To solve large scale 3-D non-stationary incompressible flow problems, an algorithm to perform an Incomplete Balancing Domain Decomposition (IBDD) is constructed in this work; as an improvement of the Balancing Domain Decomposition (BDD) method, it reduce the computation cost of the coarse problem by replacing the exact balancing procedure with an inexact balancing procedure; the nonlinear convection term of the Navier-Stokes equation is approximated by a characteristic-curve method, which is advantageous as it renders the matrix for linear equations symmetric, thus enabling the Conjugate Gradient (CG) method to be used together with the Schur complement system of Domain Decomposition Method (DDM); the algorithms are all implemented in parallel by the Hierarchical Domain Decomposition Method (HDDM) system, and the program provides solvability for models of over 10 million degrees of freedom (DOF).

412 メッシュ細分割を用いた階層型領域分割法のための大規模並列メッシュ生成法(OS4. 大規模並列・連成解析と関連話題(3),オーガナイズドセッション講演)

In this paper, a fast generation method of huge mesh for the hierarchical domain decomposition method implemented in open source software ADVENTURE is presented. In our method, a huge mesh is generated by subdividing an initial medium-sized mesh. Additionally. the mesh subdivision and the domain decomposition using METIS are alternately performed, because the domain decomposition structure of two layers called "part" and "subdomain" is required in the hierarchical domain decomposition method.

部分領域問題にＡ－ｐ法を用いた３次元非線形静磁場問題の大規模並列解析

This paper deals with large-scale 3D non-linear magnetostatic analysis by Hierarchical Domain Decomposition Method (HDDM). In magnetostatic numerical analysis, the computational object is always made in a complicated way at a large scale, and computational time is always very large. But, with the development of computational capabilities, it is now possible to focus our attention on the computational time without worrying about the amount of memory. In this paper, we reexamine the solution strategy for Finite Element Analysis (FEA) in the subdomain problem. Because the equation is singular, it has been solved by the CG (Conjugate Gradient) method in past researches. To solve it by the direct method, we introduce the A-p method into the subdomain problem. In this method we can expect to analyze more complex objects in relatively short time.

Non-linear Magnetostatic Analysis of a 100 Million DOF Problem with Hierarchical Domain Decomposition Method

Non-linear Magnetostatic Analysis of a 100 Million DOF Problem with Hierarchical Domain Decomposition Method