MLFMA-FFT Parallel Algorithm for the Solution of Extremely Large Problems in Electromagnetics

The support of range, segment and rectangle queries are fundamental problems in computational geometry, and have extensive applications in many domains. Despite significant theoretical work on these problems, efficient implementations can be complicated, and most implementations do not have useful theoretical bounds. In this paper, we focus on simple and efficient parallel algorithms and implementations for range, segment and rectangle queries, which have worst-case bounds in theory and good performance in practice, both sequentially and in parallel. We propose to use a framework based on the abstract data type augmented map, to model the problems. Based on the augmented map interface, we develop both multi-level tree structures and sweepline algorithms supporting range, segment and rectangle queries in two dimensions. For the sweepline algorithms, we also propose a parallel paradigm and show corresponding cost bounds. Theoretically, the construction algorithms of all of our data structures are work-efficient and highly parallelized.We have implemented all the data structures described in the paper, ten in all, using a parallel augmented map library. Based on the library, each data structure only requires about 100 lines of C++ code. We test their performance on large data sets (up to 108 elements) and a machine with 72-cores (144 hyperthreads). The parallel construction achieves 32-68x speedup, and the speedup numbers for queries are up to 126-fold. Sequentially, each of our implementations outperforms the CGAL library by at least 2x in both construction and queries. Our sequential implementation has approximately the same construction time as the R-tree in the Boost library, but has significantly better query performance (1.6-1200x). We believe this paper provides the most comprehensive experimental study of data structures on range, segment and rectangle queries, both in parallel and sequential setting.

In this paper, we study efficient parallel implementation for hybrid iterative methods BiCGSTAB and BiCGSTAB (l) with l = 2 on the CRAY C90, and the efficiency of their parallel performance is evaluated. Numerical experiments suggest that on the CRAY C90 a parallel inner product algorithm called PDOTB be used for the parallelization of hybrid iterative methods containing sensitive values of inner products. Lastly, it is shown that the number of iterations in which parallel hybrid iterative methods satisfy a certain convergence criterion depends on the number of processors to be used.

Hashing techniques have long been used to efficiently store and locate data indexed by key. Recently, parallel hashing algorithms have been developed that allow table insertion of many keys in a few parallel steps. The analyses of these algorithms have focused on the expected number of steps required, ignoring the issue of work complexity. As a result, these algorithms have not been work efficient. In this paper, we present a parallel hashing algorithm that is shown to be work efficient because it performs no more work than its serial counterpart. An analysis of its behavior shows that it performs S = O(log n) expected parallel steps and W = O(n) expected work. Many parallel algorithms can make use of hashing as a core step. Procedures such as histogramming, set difference, keyed reduction and dictionary lookup can be formulated using a general hash routine. Thus, parallel hashing is an important fundamental parallel operation. The above applications may also be implemented using sorting as the core step. While the use of parallel hashing has been generally accepted in the folklore of parallel computing, a dearth of literature about the expected performance of such algorithms has led many to favor the use of sorting. This paper sheds light on the performance that may be achieved using parallel hashing algorithms and should lend credibility to their use. Performance data collected from an implementation of our algorithms on the Connection Machine CM-2 and CRAY Y-MP show that it is faster than sorting by up to a factor of four on both machines. These data show that the total time required by the algorithm is more closely related to the amount of work performed, rather than the parallel step count. Our results indicate that work efficiency is an important consideration when trying to achieve high performance on parallel machines.

Unlocking massively parallel spectral proper orthogonal decompositions in the PySPOD package

A new method to retrieve aerosol optical thickness from satellite images on a parallel system

A hybrid parallel scheme for the ensemble square root filter (EnSRF) suitable for parallel assimilation of multiscale observations, including those from dense observational networks such as those of radar, is developed based on the domain decomposition strategy. The scheme handles internode communication through a message passing interface (MPI) and the communication within shared-memory nodes via Open Multiprocessing (OpenMP) threads. It also supports pure MPI and pure OpenMP modes. The parallel framework can accommodate high-volume remote-sensed radar (or satellite) observations as well as conventional observations that usually have larger covariance localization radii. The performance of the parallel algorithm has been tested with simulated and real radar data. The parallel program shows good scalability in pure MPI and hybrid MPI–OpenMP modes, while pure OpenMP runs exhibit limited scalability on a symmetric shared-memory system. It is found that in MPI mode, better parallel performance is achieved with domain decomposition configurations in which the leading dimension of the state variable arrays is larger, because this configuration allows for more efficient memory access. Given a fixed amount of computing resources, the hybrid parallel mode is preferred to pure MPI mode on supercomputers with nodes containing shared-memory cores. The overall performance is also affected by factors such as the cache size, memory bandwidth, and the networking topology. Tests with a real data case with a large number of radars confirm that the parallel data assimilation can be done on a multicore supercomputer with a significant speedup compared to the serial data assimilation algorithm.

A massively parallel fractional step solver for incompressible flows

In this paper, the possibilities of flnding out surface plasmons in negative-permittivity metamaterial scatterers, using surface integral equations, are discussed. Electrostatic resonances manifest themselves as very high values of the polarizability for a certain (negative) value of the permittivity. Another way to locate the position of the resonances is to calculate the eigenvalues of the source-free integral equation operator for the static potential on the surface of the particle. DOI: 10.2529/PIERS060906073935

The rapid development of communication systems and the impending traffic congestion of RF spectrum have led to an expansion in frequency usage towards the millimeter wave and sub-millimeter wave bands. In dealing with high frequency spectra in these bands, the conventional fabrication technology for microwave integrated circuit (MWIC) such as microstrip technology no longer applies, primarily because of high transmission loss. Although low-loss transmission media such as dielectric waveguide structures can be used as alternatives, they are difficult to fabricate and integrate with passive or active devices. This results in a growing interest in combining the advantages of microstrip and dielectric waveguide technologies. One of the most common implementations of interconnecting these two dissimilar structures is offered by aperture coupling. The theme of this dissertation is to introduce a rigorous formulation for modeling the coupling between microstrip and open-dielectric related structures (rectangular dielectric resonator antenna and image guide) via an aperture. The model is the first major rigorous method published for analyzing such types of coupling structures. The method is based on a surface integral equation approach by which the dielectric waveguide is modeled as equivalent surface electric and magnetic currents and subsequently treated via a set of combined field integral equations (CFIE). The microstrip structure and the associated coupling mechanism are formulated using the mixed potential integral equation (MPIE) approach. The coupled integral equations are then solved by the method of moments (MoM) in the spatial domain using Galerkin's procedure. Closed-form Green's functions are employed in the calculation to enhance numerical efficiency. The model is demonstrated to be a very versatile and is a practical design tool with the ability to perform accurate full-wave analysis very efficiently. The key to formulating 3-D open-dielectric waveguide structures is the introduction of the hybrid basis functions technique for modeling propagating and scattered fields associated with a guiding structure. It is based on the use of a combination of sub-domain (rooftop) and travelling wave basis functions to represent the irregular and modal surface currents on the dielectric. The technique was first applied to a 2-D planar guided structure (microstrip leaky wave antenna) before it was expanded to the 3-D geometry. The consequence of this technique is far-reaching as it has made possible a MoM analysis of 3-D finite open-dielectric waveguides that has not been reported.

The frequency-dependent resistance and inductance of uniform transmission lines are calculated with a hybrid technique that combines a cross-section coupled circuit method with a surface integral equation approach. The coupled circuit approach is most applicable for low-frequency calculations, while the integral equation approach is best for high frequencies. The low-frequency method consists in subdividing the cross section of each conductor into triangular filaments, each with an assumed uniform current distribution. The high-frequency method expresses the resistance and inductance of each conductor in terms of the current normal to the surface. An interpolation between the results of these two methods gives very good results over the entire frequency range, even when few basis functions are used. Results for a variety of configurations are shown and are compared with experimental data and other numerical techniques. >

This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems.

We present an experimental study of parallel biconnected components algorithms employing several fundamental parallel primitives, e.g., prefix sum, list ranking, sorting, connectivity, spanning tree, and tree computations. Previous experimental studies of these primitives demonstrate reasonable parallel speedups. However, when these algorithms are used as subroutines to solve higher-level problems, there are two factors that hinder fast parallel implementations. One is parallel overhead, i.e., the large constant factors hidden in the asymptotic bounds; the other is the discrepancy among the data structures used in the primitives that brings non-negligible conversion cost. We present various optimization techniques and a new parallel algorithm that significantly improve the performance of finding biconnected components of a graph on symmetric multiprocessors (SMPs). Finding biconnected components has application in fault-tolerant network design, and is also used in graph planarity testing. Our parallel implementation achieves speedups up to 4 using 12 processors on a Sun E4500 for large, sparse graphs, and the source code is freely-available at our Web site.

The second half of the 1990s has witnessed the development of two important concepts in computational sciences. First, the fast multipole method (FMM) and its multilevel variants (MLFMA) have evolved into a powerful technique allowing researchers to solve large scale problems in electromagnetics. The other is in the area of commodity parallel computing. The development of fast but inexpensive microprocessors, the evolution of Linux as a reliable and efficient operating system, and message passing standards (MPI) have prompted various researchers to construct inexpensive high performance parallel computers from commodity components. By combining the two technologies, that of the MLFMA and the commodity parallel computers, one can solve large scale electromagnetic simulations fairly inexpensively. However, in order to exploit the computing power offered by a cluster of personal computers, efficient parallel implementations of MLFMA using the message passing paradigm have to be developed. We have previously developed a portable, parallel library, called ScaleME, for MLFMA for electrodynamic and acoustic integral equation solvers (Velamparambil et al., 1998). This library uses MPI for communication and has been tested successfully on a variety of parallel computers. As an attempt to solve large scale electromagnetic scattering problems on parallel computers made from commodity components using ScaleME, we previously constructed a Linux network, called the Orion cluster, from commodity components. In this paper, we demonstrate the combined power of ScaleME and Orion through a set of test problems.

The use of numerical methods for the solution of large electromagnetic (EM) problems is nowadays a common practice. Among the several available techniques, the finite difference time domain (FDTD) is one of the most frequently adopted algorithms, thanks to its versatility and its ability to deal with complex structures. Unfortunately, the method requires a huge computational effort, so that the study of large simulation domains and the investigation of many practical EM aspects cannot be afforded by using traditional computers. Also, the needs of high accuracy when the simulation domain is modeled, implies small mesh size, with a non-negligible impact on the memory requirement if a uniform mesh scheme is adopted. The proposed variable mesh FDTD (VM-FDTD) algorithm allows a natural and efficient parallel implementation, guaranteeing the possibility of managing large memory requirements. Results on relevant topics such as the antennas characterization and the interaction between humans and EM sources are investigated, demonstrating its ability to deal with complex EM problems.

An efficient parallel algorithm is presented for computing selected components of $A^{-1}$ where A is a structured symmetric sparse matrix. Calculations of this type are useful for several applications, including electronic structure analysis of materials in which the diagonal elements of the Green's functions are needed. The algorithm proposed here is a direct method based on a block $LDL^T$ factorization. The selected elements of $A^{-1}$ we compute lie in the nonzero positions of $L+L^T$. We use the elimination tree associated with the block $LDL^T$ factorization to organize the parallel algorithm, and reduce the synchronization overhead by passing the data level by level along this tree using the technique of local buffers and relative indices. We demonstrate the efficiency of our parallel implementation by applying it to a discretized two dimensional Hamiltonian matrix. We analyze the performance of the parallel algorithm by examining its load balance and communication overhead, and show that our parallel implementation exhibits an excellent weak scaling on a large-scale high performance distributed-memory parallel machine.