Parallel Domain Research Articles

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.

A parallel space-time domain decomposition method for unsteady source inversion problems

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknowns. The three systems have to be solved one after another. These sequential steps are not desirable for large scale parallel computing. A space-time restrictive additive Schwarz method is proposed for a fully implicit space-time coupled discretization scheme to recover the time-dependent pollutant source intensity functions. We show with numerical experiments that the scheme works well with noise in the observation data. More importantly it is demonstrated that the parallel space-time Schwarz preconditioner is scalable on a supercomputer with over $10^3$ processors, thus promising for large scale applications.

Homology Models of the Trimeric CNG Channel C-Leucine Zipper Domains Offer Insight about the Olfactory CNG Channel Subunit Stoichiometry

CNG channels in rod, cone and olfactory sensory neurons are tetrameric proteins composed of A-type and B-type subunits. The subunit compositions of rod and cone photoreceptors are 3:1 CNGA1:CNGB1 and CNGA3:CNGB3, respectively. A parallel 3-helix coiled-coil domain in the carboxy-terminal leucine zipper (CLZ) region of CNGA1 constrains the channel to incorporate a single CNGB1 subunit. High-resolution crystal structures of soluble trimeric CLZ domains from CNGA1 and CNGA3 were similar and support the idea that the trimeric CLZ domain governs rod and cone subunit stoichiometry (Shuart et al. 2011 doi:10.1038/ncomms1466). By contrast, olfactory neurons have a subunit composition of 2:1:1 of CNGA2:CNGA4:CNGB1b. We used the X-ray structures of the CNGA1 and CNGA3 CLZ domains to construct a homo-trimeric CNGA2 and a hetero-trimeric CNGA2:CNGA4 (2:1) model using probablistic protein design. Once the homology models were constructed, the energies of the structures were minimized to equilibrate the systems. The potential energies of the systems after equilibration serve as a baseline reference point to quantify the overall stability of each structure. The potential energies from CNGA1, CNGA2, CNGA3 and CNGA2/CNGA4 were compared, and the heterotrimer was shown to have a more favorable structure than the homotrimers. We then performed energetic calculations using robust classical methods. The results reinforced the hypothesis that the heterotrimeric CNGA2/CNGA4 CLZ structure is the thermodynamically favored configuration. This approach was used to examine achromatopsia-associated mutations in the CLZ region of the cone CNGA3 channel subunit. The results and implications from the modeling will be presented in the context of achromatopsia pathophysiology.

A SIMPLE NANOSCALE PLASMONIC SQUARE-SHAPED RING RESONATOR WAVEGUIDE

A novel surface plasmon based square-shaped ring resonator with bending metal-dielectric- metal input/output (I/O) waveguide at optical spectral range is investigated. The influence of various geometric parameters is studied in detail, with parallel finite difference time domain method. The results validate that vertical coupling disturbance can be efficiently suppressed by employing the modified I/O structure. The transmittance performance has all the resonant frequencies workable with better extinction ratios, higher finesse and higher Q-factors compared to the original plasmonic micro-ring resonator. From these analyses, it is found that the proposed waveguide is outstanding in aspects of the total field extinction and frequency selectivity characteristic.

Parallel Domain Decomposition for 1-D Active Thermal Control Problem with PVM

this paper describes a 1-D Active Thermal Control Problem (1-D ATCP) with the use of Stationary Iterative Techniques (Jacobi and Gauss-Seidel) on the discretization of the resulted matrices. Parallelization of the problem is carried out using Domain Decomposition (DD) parallel communication approach with Parallel Virtual Machine (PVM) to enable better flexibility in parallel execution, and greater ease of parallel implementation across the different domain of block sizes. We described the parallelization of the method by the use of Single Program Multiple Data (SPMD) technique. The 1-D ATCP is implemented on a parallel cluster (Geo Cluster), with the ability to exploit inherent parallelism of the computation. The parallelization and performance strategies are discussed, and results of the parallel experiments are presented.

Density bounds for outer parallel domains of unit ball packings

We give upper bounds for the density of unit ball packings relative to their outer parallel domains and discuss their connection to contact numbers. Also, packings of soft balls are introduced and upper bounds are given for the fraction of space covered by them.

Density Bounds for Outer Parallel Domains of Unit Ball Packings

Density Bounds for Outer Parallel Domains of Unit Ball Packings

Parallel Domain Decomposition Based Distributed State Estimation for Large-scale Power Systems

Growing system sizes and complexity, along with the large amount of data provided by phasor measurement units (PMUs), are the drivers to accurate state estimation algorithms for online monitoring and operation of power systems. In this paper, a distributed weighted-least-square state estimation method using an additive Schwarz domain decomposition technique is proposed to reduce the computational execution time. The proposed approach divides a data set into several subsets to be processed in parallel using a multiprocessor architecture considering data exchange among distributed areas. The slow coherency method and balanced partitioning are utilized to reduce the communication overhead and increase accuracy. Moreover, bad data analysis is also investigated in a distributed manner. The performance of the proposed distributed state estimator, along with the speed-up for several test systems, was compared with the traditional centralized state estimator. The simulation results show a speed-up of 6.5 for a 4992-bus system.

A Practical Factorization of a Schur Complement for PDE-Constrained Distributed Optimal Control

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver--FETI-DPH--for the solution of the subproblems with the complex factors. Numerical properties of FETI-DPH in this context are demonstrated, including numerical and parallel scalability and regularization dependence. The new factorization can be used to solve Schur complement systems arising in both range-space and full-space formulations. In both cases, numerical results indicate that the complex factorization is promising. Especially, in the full-space method with the new factorization, the number of iterations required for convergence is independent of regularization parameter values.

Domain Structure of Potassium‐Sodium Niobate Ceramics Before and After Poling

Domain structure and domain wall motion play important roles on the piezoelectric properties of ferroelectric ceramics. In this work, the domain structure of hot‐pressed (K0.50Na0.50)NbO3 (KNN) ceramics before and after poling were studied by observing the domain patterns with an acid‐etching technique, and the extrinsic contribution to the piezoelectric properties were evaluated. It was found that the domain structure of the unpoled KNN ceramic was relatively complicated with many watermark, herringbone and zigzag patterns, while only a single set or few sets of parallel domain stripes were observed in the poled KNN ceramic, due to the domain reorientation and domain wall motion during the poling process. The average domain width changes from 200 (±10) nm before poling to 250 (±10) nm after poling. Domain configurations of “Herringbone‐Zigzag‐Watermark” and “Herringbone‐ Herringbone‐Zigzag” types observed in the unpoled KNN ceramic were then further analyzed. The extrinsic contribution to the piezoelectric properties from the domain reorientation and irreversible domain wall motion in the hot‐pressed KNN ceramic was found to be 71%, slightly higher than that of conventional sintered KNN ceramics ~68%.

High performance computing for flood simulation using Telemac based on hybrid MPI/OpenMP parallel programming

Usually simulations on environment flood issues will face the scalability problem of large scale parallel computing. The plain parallel technique based on pure MPI is difficult to have a good scalability due to the large number of domain partitioning. Therefore, the hybrid programming using MPI and OpenMP is introduced to deal with the issue of scalability. This kind of parallel technique can give a full play to the strengths of MPI and OpenMP. During the parallel computing, OpenMP is employed by its efficient fine grain parallel computing and MPI is used to perform the coarse grain parallel domain partitioning for data communications. Through the tests, the hybrid MPI/OpenMP parallel programming was used to renovate the finite element solvers in the BIEF library of Telemac. It was found that the hybrid programming is able to provide helps for Telemac to deal with the scalability issue.

Parallel domain decomposition method with non-blocking communication for flow through porous media

This paper introduces a domain decomposition method for numerically solving the Stokes equation for very large, complex geometries. Examples arise from realistic porous media. The computational method is based on the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which uses a finite-differences approach for discretizing the underlying equations. It achieves comparable speed and efficiency as lattice Boltzmann methods. The domain decomposition method splits a large three-dimensional region into slices that can be processed in parallel on multi-processor computation environments with only minimal communication between the computation nodes. With this method, the flow through a porous medium with grid sizes up to 20483 voxel has been calculated.

Entering the blue: conflict resolution and prevention at sea off the coast of East Africa

Scholarly work on maritime peacekeeping and responses to maritime insecurity increased notably in the early twenty-first century with much attention turning to Africa's maritime landscape. Africa's offshore security governance became particularly salient as a result of threats to good order at sea as well as how actors in the international system responded. One way of describing the responses to Africa's maritime domain is to view it as part of the response continuum depicting conflict prevention and conflict resolution. Security arrangements at sea depict a growing recognition of the importance of Africa's oceans to the extent that the landward focus of many leaders and security actors has gained a parallel domain – that of maritime security. Thrust upon the wider African security agenda by piracy off East Africa, the importance of the African maritime landscape dawned not only upon the international community and the UN in particular, but the African leadership as well. Threats at sea around Africa have an umbilical connection to what transpires on land and are equally complex to deal with. In a certain way, as suggested in this piece, reactions to promote maritime security governance off eastern Africa have become part of the wider conflict resolution agendas of actors as displayed off the Horn of Africa and in waters of the Southern African Development Community (SADC) further to the south.

Temperature dependence of static and dynamic magnetic properties in NiFe/IrMn bilayer system

Abstract

Kinetics of 90° domain wall motions and high frequency mesoscopic dielectric response in strained ferroelectrics: a phase-field simulation.

The dielectric and ferroelectric behaviors of a ferroelectric are substantially determined by its domain structure and domain wall dynamics at mesoscopic level. A relationship between the domain walls and high frequency mesoscopic dielectric response is highly appreciated for high frequency applications of ferroelectrics. In this work we investigate the low electric field driven motion of 90°-domain walls and the frequency-domain spectrum of dielectric permittivity in normally strained ferroelectric lattice using the phase-field simulations. It is revealed that, the high-frequency dielectric permittivity is spatially inhomogeneous and reaches the highest value on the 90°-domain walls. A tensile strain favors the parallel domains but suppresses the kinetics of the 90° domain wall motion driven by electric field, while the compressive strain results in the opposite behaviors. The physics underlying the wall motions and thus the dielectric response is associated with the long-range elastic energy. The major contribution to the dielectric response is from the polarization fluctuations on the 90°-domain walls, which are more mobile than those inside the domains. The relevance of the simulated results wth recent experiments is discussed.

A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator

The Helmholtz equation governing wave propagation and scattering phenomena is difficult to solve numerically. Its discretization with piecewise linear finite elements results in typically large linear systems of equations. The inherently parallel domain decomposition methods constitute hence a promising class of preconditioners. An essential element of these methods is a good coarse space. Here, the Helmholtz equation presents a particular challenge, as even slight deviations from the optimal choice can be devastating.In this paper, we present a coarse space that is based on local eigenproblems involving the Dirichlet-to-Neumann operator. Our construction is completely automatic, ensuring good convergence rates without the need for parameter tuning. Moreover, it naturally respects local variations in the wave number and is hence suited also for heterogeneous Helmholtz problems. The resulting method is parallel by design and its efficiency is demonstrated on 2D homogeneous and heterogeneous numerical examples.

CPU 클러스터 구축 및 3차원 공간분할 병렬 FDTD 알고리즘 구현

본 연구에서는 빠르게 전자파 해석을 수행할 수 있는 병렬 유한차분 시간영역(Finite-Difference Time-Domain: FDTD) 알고리즘을 구현하기 위하여 CPU 클러스터를 구축하였다. 병렬 FDTD 알고리즘은 단일 프로세서를 이용한 FDTD 알고리즘에 비해 해석 시간을 크게 줄일 수 있으며, 전기적으로 매우 큰 구조물에 대한 전자파 해석도 가능하다. 본 연구팀에서는 CPU 클러스터 기반의 병렬 FDTD 알고리즘에서 요구되는 프로세스 간의 통신을 위해 MPI(Message Passing Interface) 라이브러리를 이용하였으며, 3차원 공간분할을 적용하여 프로세스 간의 통신 시간을 최소화하였다. 단일 프로세서를 이용한 FDTD 알고리즘 대비 CPU 클러스터 기반의 병렬 FDTD 알고리즘의 계산속도 향상도를 기본 모드와 하이퍼 모드에서 분석하였으며, 전기적으로 매우 큰 콘크리트 구조물의 전자파 해석을 하였다. In this work, we construct a CPU cluster to implement a parallel finite-difference time domain(FDTD) algorithm for fast electromagnetic analyses. This parallel FDTD algorithm can reduce the computational time significantly and also analyze electrically larger structures, compared to a single FDTD counterpart. The parallel FDTD algorithm needs communication between neighboring processors, which is performed by the MPI(Message Passing Interface) library and a 3-D domain decomposition is employed to decrease the communication time between neighboring processors. Compared to a single-processor FDTD, the speed up factor of a-CPU-cluster-based parallel FDTD algorithm is investigated for the normal mode and the hypermode and finally analyze an electrically large concrete structure by the developed parallel algorithm.

Quantitative phase microscopy with off-axis optical coherence tomography

We have developed a modality for quantitative phase imaging within spectral domain optical coherence tomography based on using an off-axis reference beam. By tilting the propagation of the reference beam relative to that of the sample beam, a spatially varying fringe is generated. Upon detection of this fringe using a parallel spectral domain scheme, the fringe can be used to separate the interference component of the signal and obtain the complex sample field. In addition to providing quantitative phase measurements within a depth resolved measurement, this approach also allows elimination of the complex conjugate artifact, a known limitation of spectral interferometry. The principle of the approach is described here along with demonstration of its capabilities using technical samples.

Measurement of magnetization using domain compressibility in CoFeB films with perpendicular anisotropy

We present a method to map the saturation magnetization of soft ultrathin films with perpendicular anisotropy, and we illustrate it to assess the compositional dependence of the magnetization of CoFeB(1 nm)/MgO films. The method relies on the measurement of the dipolar repulsion of parallel domain walls that define a linear domain. The film magnetization is linked to the field compressibility of the domain. The method also yields the minimal distance between two walls before their merging, which sets a practical limit to the storage density in spintronic devices using domain walls as storage entities.

Real-time imaging with radial GRAPPA: Implementation on a heterogeneous architecture for low-latency reconstructions

Combination of non-Cartesian trajectories with parallel MRI permits to attain unmatched acceleration rates when compared to traditional Cartesian MRI during real-time imaging. However, computationally demanding reconstructions of such imaging techniques, such as k-space domain radial generalized auto-calibrating partially parallel acquisitions (radial GRAPPA) and image domain conjugate gradient sensitivity encoding (CG-SENSE), lead to longer reconstruction times and unacceptable latency for online real-time MRI on conventional computational hardware. Though CG-SENSE has been shown to work with low-latency using a general purpose graphics processing unit (GPU), to the best of our knowledge, no such effort has been made for radial GRAPPA. Radial GRAPPA reconstruction, which is robust even with highly undersampled acquisitions, is not iterative, requiring only significant computation during initial calibration while achieving good image quality for low-latency imaging applications. In this work, we present a very fast, low-latency, reconstruction framework based on a heterogeneous system using multi-core CPUs and GPUs. We demonstrate an implementation of radial GRAPPA that permits reconstruction times on par with or faster than acquisition of highly accelerated datasets in both cardiac and dynamic musculoskeletal imaging scenarios. Acquisition and reconstruction times are reported.