Showing papers presented at "Conference on Scientific Computing in 2010"

Generic implementation of finite element methods in the distributed and unified numerics environment (dune)

Abstract: In this paper we describe PDELAB, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (DUNE). PDELAB considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying polynomial degree. The underlying DUNE software framework provides parallelization and dimension-independence.

A unified discrete-continuous sensitivity analysis method for shape optimization

Abstract: Boundary shape optimization problems for systems governed by partial differential equations involve a calculus of variation with respect to boundary modifications. As typically presented in the literature, the first-order necessary conditions of optimality are derived in a quite different manner for the problems before and after discretization, and the final directional-derivative expressions look very different. However, a systematic use of the material-derivative concept allows a unified treatment of the cases before and after discretization. The final expression when performing such a derivation includes the classical before-discretization (“continuous”) expression, which contains objects solely restricted to the design boundary, plus a number of “correction” terms that involve field variables inside the domain. Some or all of the correction terms vanish when the associated state and adjoint variables are smooth enough.

All-at-once preconditioning in pde-constrained optimization

Abstract: The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques.

4d embryogenesis image analysis using pde methods of image processing

Abstract: In this paper, we introduce a set of methods for processing and analyzing long time series of 3D images representing embryo evolution. The images are obtained by in vivo scanning using a confocal microscope where one of the channels represents the cell nuclei and the other one the cell membranes. Our image processing chain consists of three steps: image filtering, object counting (center detection) and segmentation. The corresponding methods are based on numerical solution of nonlinear PDEs, namely the geodesic mean curvature flow model, flux-based level set center detection and generalized subjective surface equation. All three models have a similar character and therefore can be solved using a common approach. We explain in details our semi-implicit time discretization and finite volume space discretization. This part is concluded by a short description of parallelization of the algorithms. In the part devoted to experiments, we provide the experimental order of convergence of the numerical scheme, the validation of the methods and numerous experiments with the data representing an early developmental stage of a zebrafish embryo.

Numerical algorithms for perspective shape from shading

Abstract: The Shape-From-Shading (SFS) problem is a fundamental and classic problem in computer vision. It amounts to compute the 3-D depth of objects in a single given 2-D image. This is done by exploiting information about the illumination and the image brightness. We deal with a recent model for Perspective SFS (PSFS) for Lambertian surfaces. It is defined by a Hamilton-Jacobi equation and complemented by state constraints boundary conditions. In this paper we investigate and compare three state-of-the-art numerical approaches. We begin with a presentation of the methods. Then we discuss the use of some acceleration techniques, including cascading multigrid, for all the tested algorithms. The main goal of our paper is to analyze and compare recent solvers for the PSFS problem proposed in the literature.

A Minimal Spatial Cellular Automata for Hierarchical Predatory Prey Simulation of Food Chains.

Abstract: Models of complex spatial environmental and ecological systems are usually constructed using partial differential equations (PDEs), but cellular automata (CA’s) can provide microscopically simple yet macroscopically rich alternatives. We develop a cellular automata model of a hierarchical predator-prey system and show that even a minimal automaton is able to capture the essential boom-bust and dynamical behaviour of real physical systems. A single probability rate of predator death is used to control predator behaviour. We describe the model in detail and explore the CA model for oneand two-predator food chains. We find a well delineated phase transition in the 2-predator system when the predator lifetime parameter is varied and present some system analysis and quantitative metrics. We discuss the CA model in comparison with PDE and more detailed event-driven agent-based models.

Cellular Automata Approach to Corrosion and Passivity Phenomena.

Abstract: Our research on employing the cellular automata methodology to corrosion and passivation phenomena is reviewed. Examples of a peculiar pit development are found and presented. The diffusion rate in the corroding medium is argued and shown in the simulation results to affect mainly the characteristic length scale for the corrosion process. New data for the pitting corrosion development on a planar interface are presented and discussed.

An Evaluation of Parallel Knapsack Algorithms on Multicore Architectures.

Abstract: Emergence of chip multiprocessor systems has dramatically increased the performance potential of computer systems. Since the amount of exploited parallelism is directly influenced by the selection of the algorithm, algorithmic choice also plays a critical role in achieving high performance on modern architectures. Hence, in the era of multicore computing, it is important to re-evaluate algorithms efficiency for key problem domains. This paper investigates the impact of algorithmic choice on the perfor mance of parallel implementations of the integral knapsack problem on multicore architectures. The study considers two algorithms and their parallel implementations, and examines several aspects of performance including speedup

Surrogate Modeling of Low Noise Amplifiers Based on Transistor Level Simulations

Abstract: Although the behavior of several RF circuit blocks can be accurately evaluated via transistor-level simulations, the design space exploration is limited by the high computational cost of such simulations. Therefore, cheap-to-evaluate surrogate models of the circuit simulator are introduced. This paper presents some results of a feasibility study concerning the development of surrogate models of low noise amplifiers.

Numerical simulation of suspension induced rheology

Abstract: Flow of particles suspended in a fluid can be found in numerous industrial processes utilizing sedimentation, fluidization and lubricated transport such as food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation The ability to understand rheology effects of particulate flows is elementary for the design, operation and efficiency of the underlying processes Despite the fact that particle technology is widely used, it is still an enormous experimental challenge to determine the correct parameters for the process employed In this paper we present 2-dimensional numerical results for the behavior of a particle based suspension and compare it with analytically results obtained for the Stokes-flow around a single particle

Application Context of the SCIDDICA Model Family for Simulations of Flow-Like Landslides.

Abstract: Cellular Automata (CA) are parallel computing models whose evolution is governed by purely local laws. The global dynamics of complex systems simulated by means of CA emerges from the local interactions of their elementary components. Some macroscopic natural phenomena are included in the class of such complex systems. Among them, of particular interest are several W\SHVRI³VXUIDFHIORZV´ where typical examples are debris flows and lava flows. In this review paper, a methodology for modelling complex natural systems through Macroscopic Cellular Automata (MCA) is presented and applied to flow-­type landslides simulations. Specifically, we will show the SCIDDICA family models, with particular reference to the hexagonal release of MCA models for the simulation of flow-­type landslides. The models, here presented, are initially adopted for subaerial flow-­like landslides simulations, and applied recently to combined subaerial-­subaqueous flow-­like landslides.

Wentzel-Freidlin estimates for jump processes in semi-group theory: upper bound

Abstract: We give a translation in semi-group theory of Wentzel-Freidlin estimates for Poisson process. We consider the case of the upper bound.

On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations

Abstract: We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier-Stokes equations by the backward difference formula -discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss the choice of the preconditioner, stopping criterion and the choice of the time step and propose a new strategy which leads to an efficient and accurate numerical scheme.

Performance Modeling, Analysis, and Optimization of Cell-List Based Molecular Dynamics.

Abstract: We have developed a performance prediction model for non-bonded interaction computations in molecular dynamics simulations, thereby predicting the optimal cell dimension in a linked-list cell method. The model expresses computation time in terms of the number and unit computation time of key operations. The model accurately estimates the number of operations during the simulations with the maximum standard error of 10.6% compared with actual measurements. Then, the unit computation times of the operations are obtained by bisquare regression. Analysis of this model reveals that the optimal cell dimension to minimize the computation time is determined by a trade-off between decreasing search space and increasing linked-list cell access for smaller cells. The model predicts the optimal cell dimension correctly for 80% of all tested cases, resulting in an average speedup of 10% and 52% for the cutoff radius of interaction, 6.6 and 10.0 A, respectively.

Hybrid parallelization of an adaptive finite element code

Abstract: We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS.

A Parallel Needleman - Wunsch - Hirschberg Bio-sequence Alignment Algorithm.

Abstract: The Needleman – Wunsch (NW) algorithm is a dynamic programming method for aligning bio-sequences. Although the method is exact, bioinformatics practitioners often prefer to perform their sequence alignment with a heuristic method, the well-known BLAST. The arguments against Needleman-Wunsch are its high memory demands, a relatively slower response time, and sometimes, difficulties in producing a load-balanced parallelization. Memory demands have been alleviated with a variant based on Hirschberg longest common sequence identification algorithm, which we refer as the Needleman–Wunsch–Hirschberg (NWH) algorithm. NWH trades memory by computations, but preserving the O(n 2 ) time complexity bound of NW. Its parallelization however, is even more challenging than that of the NW algorithm. This paper discusses an intermediate approach, which we called parallel Needleman-WunschHirschberg (PNWH). PNWH keeps memory space within reasonable bounds, eliminates the extra computational burden of NWH, and yields an exact load-division and balancing formula for its effective parallelization.

Large Scale VLSI Circuit Simulation Using Point Relaxation.

Abstract: The aim of this paper is to show that by using the elementary technique of point relaxation (i.e., Gauss seidel iteration of static nonlinear equations at each time point), we can solve accurately very large digital circuits of several million nodes. The characteristic of such circuits is a well defined direction of signal flow, which can be defined beforehand and used for ordering the nodes during the iteration. An attendant, and important, benefit is the relatively small requirement of storage space. We have been able to simulate MOS digital circuits with approximately 1.6 million transistors (512 × 512 SRAM memory array) in about half an hour using less than 1.3GB working memory (Pentium-4, 2.2GHz). We also propose a simple parallelization technique and experimentally demonstrate that we can solve digital circuits with tens of million transistors in a few hours.

Parallel Evolutionary Computation in Very Large Scale Eigenvalue Problems

Abstract: The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions [21]. This paper reports on new methods for finding eigenvalues of very large matrices by a synthesis of evolutionary computation, parallel programming, and empirical stochastic search. The direct design of our method has the added advantage that it could be adapted to extend many algorithmic variants of solutions of generalized eigenvalue problems to improve the accuracy of our algorithms. The preliminary evaluation results are encouraging and demonstrate the method’s efficiency and practicality.

EM Scattering Calculations Using Potentials

Abstract: EM scattering from PEC surfaces are mostly calculated through the induced surface current J. In this paper, we consider PEC surfaces homeomorphic to the sphere, apply Hodge decomposition theorem to a slightly rewritten surface current, and show how this enables us to replace the unknown current with two scalar functions which serve as potentials for the current. Implications of this decomposition are pointed out, and numerical results are demonstrated.

Predictive Modeling of Forecast Uncertainty in the Route Availability Planning Tool (RAPT).

Abstract: MIT Lincoln Laboratory has developed the Route Availability Planning Tool (RAPT), which provides automated convective weather guidance to air traffic managers of the NYC metro region. Prior studies of RAPT have shown high-accuracy guidance from forecast weather, but further refinements to prevent forecast misclassification is still desirable. An attribute set of highly correlated predictors for forecast misclassification is identified. Using this attribute set, a variety of prediction models for forecast misclassification are generated and evaluated. Rule-based models, decision trees, multi-layer perceptrons, and Bayesian prediction model techniques are used. Filtering, resampling, and attribute selection methods are applied to refine model generation. Our results show promising accuracy rates for multi-layer perceptrons trained on full attribute sets.

A Multithread Scientific Library for Complex Systems.

Abstract: Cellular Automata are parallel computing models used for the modeling and simulation of complex systems. This paper presents the latest release of libAuToti, an open-source parallel library for implementing models based on the Cellular Automata approach. The library permits a straightforward and simple implementation of Macroscopic Cellular Automata models, which are appropriate for the simulation of spatial extended dynamical systems. With the emergence of multi-processor computers, multithreaded programming is quickly gaining popularity. Therefore, the current version of the library introduces the possibility to implement multithread versions of models, in order to better exploit multi-core architectures. Scientific visualization of implemented models is also possible thanks to the adoption of a 3D interactive VTK (Visualization Toolkit) module. Experiments, performed by considering the simulation of lava flows as defined by the SCIARA model and executed both on an Intel Xeon 8 core machine and a dual-core standard PC, have demonstrated the elevated computational efficiency of the library, confirming the reliability of the library and goodness of simulation results. Future improvements and possible applications are discussed at the end of the paper.

Div-curl lemma revisited: applications in electromagnetism

Abstract: Two new time-dependent versions of div-curl results in a bounded domain Ω ⊂ ℝ 3 are presented. We study a limit of the product v k w k , where the sequences v k and w k belong to L 2 (Ω). In Theorem 2.1 we assume that V × v k is bounded in the L p -norm and ∇ · w k is controlled in the L r -norm. In Theorem 2.2 we suppose that V × w k is bounded in the Lp-norm and ∇ · w k is controlled in the L r -norm. The time derivative of w k is bounded in both cases in the norm of H -1 (Ω). The convergence (in the sense of distributions) of v k w k to the product vw of weak limits of v k and w k is shown.

Introduction to Statistical Geometry.

Abstract: By accepting the uncertainty principle in an Euclidean plane, the position of point, line, and every geometric shape can be identi…ed by the statistical parameters of mean and standard deviation. A heuristic model of Euclidean Statistical Geometry will be established. An axiomatic approach for unde…ned terms and their use in geometric objects is presented. The consistency of geometric interpretations of the mean, variance, and correlation coe¢ cient for random vectorial events in the Euclidean plane are discussed. Key Words: Euclid’s postulates, unde…ned terms, fuzzy points, fuzzy lines, belongs to, statistical

Efficiency in Computing Correlation Matrix of Wavelet Coefficients by Exploiting Index Structure.

Abstract: Abstract—Correlation matrices are ubiquitous throughout signal processing, networking and in many areas of science [1][ 2][3]. However, our study of the literature found that there is limited research on the structure of the indices in correlation matrix of wavelet coefficients, and in the exploitation of that struct ure to improve its computational efficiency. This article seeks tomake a contribution in this area. Specifically, it will be shown that four matrices of the indices of the correlation matrix of wavelet coefficients may be visualized. The matrices are of a simple structure. Two of them consists of the scaling indices of the wavelet coefficients. They are related by the transpose oper ation. The other two matrices consists of shift indices and are also related by the transpose operation. By exploiting these fac ts, an efficient method for implementing the correlation matrix of wavelet coefficients may be realized.