Parallelization of the inverse fast multipole method with an application to boundary element method
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Computer Science↗
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Results for “BOUNDARY ELEMENT METHOD”
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Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method
Here we investigate an efficient preconditioning of iterative methods (such as GMRES) for solving dense linear systems Ax = b that follow from a boundary element method (BEM) for the 3D Helmholtz equation, focusing on the low-frequency regime. While matrix–vector products in GMRES can be accelerated through the low-frequency fast multipole method (LFFMM), the BEM often remains computationally expensive due to the large number of GMRES iterations. We propose the application of the inverse fast multipole method (IFMM) as a preconditioner to accelerate the convergence of GMRES. The IFMM is in essence an approximate direct solver that uses a multilevel hierarchical decomposition and low-rank approximations. The proposed IFMM-based preconditioning has a tunable parameter ε that balances the cost to construct a preconditioner M, which is an approximation of A -1 , and the cost to perform the iterative process by means of M. Namely, using a small (respectively, large) value of ε takes a long (respectively, short) time to construct M, while the number of iterations can be small (respectively, large). A comprehensive set of numerical examples involving various boundary value problems with complicated geometries and mixed boundary conditions is presented to validate the efficiency of the proposed method. We show that the IFMM preconditioner (with a nearly optimal ε of 10 -2 ) clearly outperforms some common preconditioners for the BEM, achieving 1.2–10.8 times speed-up of the computations, in particular when the scale of the underlying scatterer is about five wavelengths or more. In addition, the IFMM preconditioner is capable of solving complicated problems (in a reasonable amount of time) that BD preconditioner can not.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Explicit structural topology optimization using boundary element method‐based moving morphable void approach
Abstract This article presents an explicit topology optimization approach using boundary element method based moving morphable void (MMV). Structural analysis in the conventional MMV approach is performed on a fixed mesh over the entire design domain. However, in the proposed method structural boundaries are described using B‐splines and discretized with boundary elements making explicit representation of the boundaries possible. In this regard, the proposed approach has following merits: a) the use of weak material, which is often adopted to mimic voids can be completely avoided; b) exact and explicit description of voids in MMV allows the capture of tiny structural features in a robust and effective way; c) numerical instabilities stemming from the use of fixed meshes can be naturally avoided. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Zhang, Weisheng↗
A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization
In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel
We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.
97 MATHEMATICS AND COMPUTING↗
An O(N logN) multi-layer boundary element method for direct computation of sound propagation in shallow water environments
Direct three-dimensional (3D) numerical simulations of acoustic fields in range-dependent shallow water environments remains a challenge due to environmental complexities and large computational cost.We develop an efficient 3D boundary element method (BEM) for shallow water acoustic propagation which utilizes a Pre-corrected Fast Fourier Transform (PFFT) approach to reduce the computational effort from O ( N 2~3 ) to O ( N log N ) where N is the total number of boundary unknowns. To account for inhomogeneous media, the method allows for arbitrary number of coupled multi-layer BEM sub-domains. With O ( N log N ) efficiency and the use of massively parallel high-performance computing platforms, we are able to conduct multi-layer 3D direct simulations of low-mid frequency acoustics over kilometer ranges. Furthermore we perform extensive validations of the method and provide two shallow water waveguide examples benchmarked against theoretical solutions. To illustrate the efficacy and usefulness of the PFFT-BEM method, we perform 3D large-scale direct simulations to assess the performance of two established canonical models: axisymmetric coupled mode model for 3D seamount; and Kirchhoff approximation and perturbation theory for 3D rough surface scattering.
42 ENGINEERING↗
Differential algebraic fast multipole-accelerated boundary element method for nonlinear beam dynamics in arbitrary enclosures
Not Available
43 PARTICLE ACCELERATORS↗
Leaky guided waves in generic bars: Numerical prediction and experimental validation by means of ultrasonic underwater testing
Guided Ultrasonic Waves (GUWs) are used in several industrial and civil applications for the non-destructive tests and inspection of mechanical waveguides immersed in fluids. As well known, the impedance mismatch at the fluid-structure interface causes the bulk waves traveling inside the waveguide to be partially refracted in the surrounding fluid. The leakage of bulk waves involves continuous energy radiation along the propagation direction, resulting in high attenuation rates and, consequently, reduced inspection ranges. In this work, the dispersion behaviour of leaky guided waves that propagate in immersed waveguides of general cross-section is investigated. To this end, a Semi-Analytical Finite Element (SAFE) method coupled with a 2.5D Boundary Element method (BEM) is used to extract the wave dispersion equation. The proposed formulation avoids the well known limitations of analytical methods in treating complex geometries as well as those of Finite Element-based methods in representing propagation processes in unbounded domains. Numerical and experimental results are presented, in which the dispersion curves are extracted for different bars of arbitrary shape immersed in water. The results obtained in this paper can be useful for the design of testing conditions in practical applications and to tune experimental set up.
42 ENGINEERING↗
A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow
Here we propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold. First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM. This unfitted boundary method permits to avoid remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary. Second, the computational effort is reduced by the development of a Reduced Order Model (ROM) technique based on a POD-Galerkin approach. Third, the SBM provides a smooth mapping from the true to the surrogate domain, and for this reason, the stability and performance of the reduced order basis are enhanced. This feature is the net result of the combination of the proposed ROM approach and the SBM. Similarly, the combination of the SBM with a projection-based ROM gives the great advantage of an easy and fast to implement algorithm considering geometrical parametrization with large deformations. The transformation of each geometry to a reference geometry (morphing) is in fact not required. These combined advantages will allow the solution of PDE problems more efficiently. We illustrate the performance of this approach on a number of two-dimensional Stokes flow problems.
42 ENGINEERING↗
A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Review of TEAMER Awards for WEC-Sim Support: Preprint
Testing Expertise and Access for Marine Energy Research (TEAMER) is a U.S. Department of Energy Water Power Technologies Office sponsored program, overseen by the Pacific Ocean Energy Trust, which aims to advance the state of marine energy technologies. The program connects technology developers with experts at U.S. facilities, including numerical modeling and analysis facilities, like WEC-Sim. The WEC-Sim facility is supported by the WEC-Sim development team at Sandia National Laboratories and the National Renewable Energy Laboratory. WEC-Sim (Wave Energy Converter SIMulator) is an open-source software for simulating wave energy converters. WEC-Sim can model the multi-body dynamics of devices comprised of bodies, joints, power take-off systems, and mooring systems. Since TEAMER's first round of support in 2020, there have been eighteen TEAMER awards focused on numerical model development in WEC-Sim. TEAMER awards for WEC-Sim support have modeled a wide range of wave energy converter archetypes, including point absorbers, attenuators, oscillating water columns, and many other novel architectures. A wide variety of studies have been conducted, leading to important insights for TEAMER partners and software improvements for WECSim. This article highlights several successful WEC-Sim TEAMER awards. The awards described herein include TEAMER recipients Ocean Motion Technologies, AquaHarmonics, iProTech, East Carolina University, Virginia Tech, Maiden Wave Energy, and the University of Massachusetts Dartmouth. The awards of these seven partners contain a wide range of investigations and cover the creation of baseline hydrodynamic models, PTO modeling, geometry optimization in both boundary element methods and WECSim, and model tuning and validation.
industry support↗
A Boundary Element Based Method for Accurate Prediction of the Surface Pressure Cross-Spectral Density Matrix.
Abstract not provided.
Rouse, Jerry W.↗
Boundary node Petrov–Galerkin method in solid structures
Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).
97 MATHEMATICS AND COMPUTING↗
X-ray CT characterization and fracture simulation of ASR damage of glass particles in alkaline solution and mortar
The alkali-silica reaction (ASR) damage in reactive aggregates affects the long-term durability of the concrete infrastructure. The generated ASR gel can expand by imbibing water from the pore solution and the resulting expansion pressure causes the aggregate fracture. This study aims to simulate the development of ASR damage in glass particles of two types of samples (glass in alkali solution and glass mortars). The dynamic micro X-ray CT technique was conducted to monitor the crack propagation in glass aggregates at different reaction stages (up to 64 hrs). The Boundary Element Method (BEM) and Displacement Discontinuity Method (DDM) were used to efficiently simulate the crack propagation within irregular glass particles under gel expansion pressures. The aggregate boundaries were built with the BEM elements and the initial cracks were meshed with the DDM elements. The estimated expansion pressure was applied to the initial crack surfaces. The discontinuous displacements and stresses were calculated along the crack path and crack tip. The mixed-mode Stress Intensity Factors (SIFs) were calculated based on plane stress conditions. The maximum circumferential stress criteria was used to simulate the propagation of cracks along a specific angle. The simulation results include the simulated crack path and the combined SIFs changing with the increments. With the estimate expansion pressure, the glass particle damages were simulated within conditions of alkali solution and confined motar samples. The predicted crack propagation path was compared with the X-ray CT imaging data. The comparison results demonstrate the DDM has the ability to predicting the ASR damage propagation inside aggregates.
36 MATERIALS SCIENCE↗
An experimental comparison of various methods of nearfield acoustic holography
An experimental comparison of four different methods of nearfield acoustic holography (NAH) is presented in this study for planar acoustic sources. The four NAH methods considered in this study are based on: (1) spatial Fourier transform, (2) equivalent sources model, (3) boundary element methods and (4) statistically optimized NAH. Two dimensional measurements were obtained at different distances in front of a tonal sound source and the NAH methods were used to reconstruct the sound field at the source surface. Reconstructed particle velocity and acoustic pressure fields presented in this study showed that the equivalent sources model based algorithm along with Tikhonov regularization provided the best localization of the sources. Reconstruction errors were found to be smaller for the equivalent sources model based algorithm and the statistically optimized NAH algorithm. Effect of hologram distance on the performance of various algorithms is discussed in detail. The study also compares the computational time required by each algorithm to complete the comparison. Four different regularization parameter choice methods were compared. The L-curve method provided more accurate reconstructions than the generalized cross validation and the Morozov discrepancy principle. Finally, the performance of fixed parameter regularization was comparable to that of the L-curve method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Multiple scattering of surface waves by cavities in a half-space
Scattering of surface waves from multiple two-dimensional cavities at the surface of a homogenous, isotropic, linearly elastic half-space is analyzed in this work. For the case of multiple cavities, the scattered field is shown to be equivalent to the total radiation from the distributions of tractions, calculated from the incident wave, over the surfaces of the cavities. The multiple-scattering model is obtained from known single-scattering calculation for a cavity by the use of the self-consistent method. The second order approximation to the multiple-scattering problem by a random distribution of cavities is then considered and solved analytically. The vertical displacement at some distance from the cavities is calculated and verified by the solution of the same problem obtained by the boundary element method (BEM). The analytical and BEM results are graphically displayed and show good agreement when the depths of the cavities are small compared to the wavelength.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗