Dynamic Domain Decomposition Method Research Articles

D 3 PBO: D ynamic D omain D ecomposition-based P arallel B ayesian O ptimization for Large-scale Analog Circuit Sizing

Bayesian optimization (BO) is an efficient global optimization method for expensive black-box functions, but the expansion for high-dimensional problems and large sample budgets still remains a severe challenge. In order to extend BO for large-scale analog circuit synthesis, a novel computationally efficient parallel BO method, D 3 PBO, is proposed for high-dimensional problems in this work. We introduce the dynamic domain decomposition method based on maximum variance between clusters. The search space is decomposed into subdomains progressively to limit the maximal number of observations in each domain. The promising domain is explored by multi-trust region-based batch BO with the local Gaussian process (GP) model. As the domain decomposition progresses, the basin-shaped domain is identified using a GP-assisted quadratic regression method and exploited by the local search method BOBYQA to achieve a faster convergence rate. The time complexity of D 3 PBO is constant for each iteration. Experiments demonstrate that D 3 PBO obtains better results with significantly less runtime consumption compared to state-of-the-art methods. For the circuit optimization experiments, D 3 PBO achieves up to 10× runtime speedup compared to TuRBO with better solutions.

Dynamic domain decomposition method based on weighted Voronoi diagrams

Dynamic load balancing during the high performance computing is an important part of parallel workflow. An efficient way to achieve the desired distribution of load during computation is to use the Voronoi diagram (VD) for the domain decomposition. The advantage of this approach is that it can be used in conjunction with various numerical methods and balancing strategies. Domain decomposition based on Voronoi diagrams can be used together with Eulerian meshes, Lagrangian meshes, and meshfree methods, such as molecular dynamic or smoothed-particle hydrodynamics (SPH). However, for the basic VD decomposition it may be difficult to obtain load balance when the adaptive mesh refinement (AMR) is used: because of the high heterogeneity of the load on the adapted mesh, the balancing algorithms may be unstable or have poor convergence.In the present study we propose an improvement of the ordinary VD domain decomposition method with using the weighted Voronoi diagrams. We demonstrate the possibilities of such domain decomposition to achieve a better balanced configuration on two- and three-dimensional problems using mesh configurations typical for computational fluid dynamics.

Implementation of the moving particle semi-implicit method for free-surface flows on GPU clusters

The moving particle semi-implicit (MPS) method performs well in simulating incompressible flows with free surfaces. Despite its applicability, the MPS method suffers from the fundamental instability problem and high computational cost in its practical application. Substantial research has been conducted on improving the stability and accuracy of the MPS method. Moreover, graphics processing units (GPUs), which are multi-processors that execute many three-dimensional geometric processes at high speed, provide unprecedented capability for scientific computations. However, the usage of a single GPU card is not sufficient for engineering applications that require several million particles that predict the desired physical processes, because the available memory space is insufficient. In this work, the dynamic stability (DS) algorithm and particle shifting (PS) algorithm have been used to overcome the instability and inaccuracies caused by tensile instability and non-uniform particle distribution, respectively. Based on the stable MPS method, a GPU-based MPS code that uses the compute unified device architecture (CUDA) language has been developed. An efficient neighborhood particle search is performed using an indirect method, and the matrix for the pressure Poisson equation (PPE) is assembled in parallel. Based on the single-GPU version, a multi-GPU MPS code has been developed. The approach uses a non-geometric dynamic domain decomposition method that provides homogeneous load balancing whereby different portions (subdomains) of the physical system under study are assigned to different GPUs. Communication between devices is achieved with the use of a message passing interface (MPI). Based on the neighborhood particle search, the techniques for building and updating the “halo” are described in detail. The speed-up of the single-GPU version is analyzed for different numbers of particles, and the scalability of the multi-GPU version is analyzed for different numbers of particles and different numbers of GPUs. Last, an application with more than 107 particles is presented to show the capability of the code in handling large-scale simulations.

Parallel adaptive mesh refinement method based on bubble-type local mesh generation

An efficient parallel adaptive mesh refinement method based on bubble-type local mesh generation (BLMG), employing ParMETIS-based dynamic domain decomposition method, is developed. The BLMG method is applied to generate the mesh with high quality, and the local mesh for each processor can be generated simultaneously without communication. The node-based distributed mesh structure is designed to reduce the communication amount spent in mesh generation and finite element calculation. To gain the load balance, a new load balancing algorithm for the new mesh structure is devised to make sure the whole algorithm is efficient. Several numerical examples are carried out to verify the high efficiency of the algorithm.

A domain decomposition strategy for hybrid parallelization of moving particle semi-implicit (MPS) method for computer cluster

The MPS is a particle method developed to simulate incompressible flows with free surfaces that has several applications in nonlinear hydrodynamics. Much effort has been done to handle the large amount of particles required for simulating practical problems with desired refinement. However, the efficient use of the currently available computational resources, such as computer cluster, remains as a challenge. The present paper proposes a new strategy to parallelize the MPS method for fully distributed computing in cluster, which enables to simulate models with hundreds of millions of particles and keeps the required runtime within reasonable limits, as shown by the analysis of scalability and performance. The proposed strategy uses a non-geometric dynamic domain decomposition method that provides homogeneous load balancing and for very large models the scalability is supra-linear. Also, the domain decomposition (DD) is carried out only in the initial setup. As a result, the DD method is based on renumbering of particles using an original fully distributed sorting algorithm. Moreover, unlike the usual strategies, none of the processors require access to global data of the particles on any time step. Therefore, the limit for the maximum size of the model depends more on the total memory of the allocated nodes than the quantity of the local memory of each node. Thus, by extending the application of MPS method to very large models, this study contributes to consolidating the method as a practical tool to investigate complex engineering problems.

Dynamic domain decomposition method and its application on nonlinear problem

In this paper, domain decomposition method (DDM) for numerical solutions of mathematical physics equations is improved into dynamic domain decomposition method (DDDM). The main feature of the DDDM is that the number, shape and volume of the sub-domains are all flexibly changeable during the iterations, so it suits well to be implemented on a reconfigurable parallel computing system. Convergence analysis of the DDDM is given, while an application approach to a weak nonlinear elliptic boundary value problem and a numerical experiment are discussed.

NUMERICAL SIMULATION OF UNSTEADY FLOW FIELD AROUND HELICOPTER IN FORWARD FLIGHT USING A PARALLEL DYNAMIC OVERSET UNSTRUCTURED GRIDS METHOD

A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.

Domain Decomposition of Optimal Control Problems for Dynamic Networks of Elastic Strings

We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d^3m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.