Hierarchical Domain Decomposition Research Articles

GENESIS CGDYN: large-scale coarse-grained MD simulation with dynamic load balancing for heterogeneous biomolecular systems.

Residue-level coarse-grained (CG) molecular dynamics (MD) simulation is widely used to investigate slow biological processes that involve multiple proteins, nucleic acids, and their complexes. Biomolecules in a large simulation system are distributed non-uniformly, limiting computational efficiency with conventional methods. Here, we develop a hierarchical domain decomposition scheme with dynamic load balancing for heterogeneous biomolecular systems to keep computational efficiency even after drastic changes in particle distribution. These schemes are applied to the dynamics of intrinsically disordered protein (IDP) droplets. During the fusion of two droplets, we find that the changes in droplet shape correlate with the mixing of IDP chains. Additionally, we simulate large systems with multiple IDP droplets, achieving simulation sizes comparable to those observed in microscopy. In our MD simulations, we directly observe Ostwald ripening, a phenomenon where small droplets dissolve and their molecules redeposit into larger droplets. These methods have been implemented in CGDYN of the GENESIS software, offering a tool for investigating mesoscopic biological processes using the residue-level CG models.

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

Meta-scalable discriminate analytics for Big hyperspectral data and applications

Recent technology developments in hyperspectral sensing has made it possible to acquire several hundred spectral bands that cover the electromagnetic spectrum of an observational scene in a single acquisition. The resulting hyperspectral data cube contains a large volume of spatial-spectral information. It has several concrete and special characteristics such as being multi-source, multi-scale, high dimensional and nonlinear. The hyperspectral video with temporal information further increases the data generation velocity and volume which lead to the Big data challenges especially in remote sensing applications. We term this type of Big data as Big hyperspectral data to differentiate it from the Big data generated from internet and multimedia-based sources. This paper presents a novel data computation framework for Big hyperspectral data discriminate analytics. This framework consists of some essential modules like tree-based divide-conquer (Tree-DC) mechanism, hierarchical spatial-spectral domain (HSSD) decomposition, global scalable and locally fast discriminative analytics (GSLF-DA), tree-based divide-conquer-merge (DCM), and temporal hyperspectral data decomposition. The challenge of the framework is to sustain the divide-conquer scalability for implementation on rapidly evolving parallel computing architectures i.e., transforming the divide-conquer mechanism to be meta-scalable. Moreover, the discriminate analytics in conjunction with the proposed mechanism can give the optimal solution in the final merging stage. Experiments are performed to validate the performance of the mechanisms in the framework.

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.

Development of Hierarchical Domain Decomposition Explicit MPS Method and Application to Large-scale Tsunami Analysis with Floating Objects

Development of Hierarchical Domain Decomposition Explicit MPS Method and Application to Large-scale Tsunami Analysis with Floating Objects

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.

An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.

Application of the hierarchical domain decomposition boundary element method to the simplified P3 equation

In this paper, the hierarchical domain decomposition boundary element method (HDD-BEM), which has been developed to solve the diffusion equation, is applied to the simplified P3 (SP3) equation. The HDD-BEM solution for the SP3 equation is provided in the present paper. A computer program, ABEMIE, based on the HDD-BEM is developed, and a two-dimensional one-group anisotropic-scattering benchmark problem is solved with it to verify the present HDD-BEM for the SP3 equation.Through numerical benchmarking, it is shown that the present method results in good agreement with the solution obtained using the existing SPN solver based on the finite element method for both eigenvalue and neutron flux distribution. This benchmark result suggests that the HDD-BEM is suitable for application to the SPN equation.

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.