Qifu Wang

Graphics processing unit (GPU) accelerated fast multipole BEM with level-skip M2L for 3D elasticity problems

GPU parallel algorithm of the fast multipole BEM with level-skip M2L is presented.A rigid body motion method for the fast multipole BEM is given.Different M2L schemes are compared and discussed in detail.Engineering examples demonstrate the efficiency and accuracy of the algorithm. In order to accelerate fast multipole boundary element method (FMBEM), in terms of the intrinsic parallelism of boundary elements and the FMBEM tree structure, a series of CUDA based GPU parallel algorithms for different parts of FMBEM with level-skip M2L for 3D elasticity are presented. A rigid body motion method (RBMM) for the FMBEM is proposed based on special displacement boundary conditions to deal with strongly singular integration and free term coefficients. The numerical example results show that our parallel algorithms obviously accelerates the FMBEM and can be used in large scale engineering problems with wide applications in the future.

Sparsity-promoting polynomial response surface: A new surrogate model for response prediction

Abstract Computation-intensive analyses/simulations are becoming increasingly common in engineering design problems. To improve the computation efficiency, surrogate models are used to replace expensive simulations of engineering problems. This paper proposes a new high-fidelity surrogate modeling approach which is called the Sparsity-promoting Polynomial Response Surface (SPPRS). In the SPPRS model, a series of Legendre polynomials is selected as basis functions, and its number is compatible with the sample size so as to enhance the expression ability for complex functional relationships. The coefficients associated with basis functions are estimated using a “sparsity-promoting” regression approach which is an ensemble of two techniques: least squares and l 1 -norm regularization. As a result, only these basis functions relevant to explain the function relationship are picked out, and that dedicates to ease the problem of overfitting for training points. With the sparsity-promoting regression approach, such a surrogate model intends to capture both the global trend of the functional variation and a reasonable local accuracy in the neighborhood of training points. Additionally, Latin hypercube design (LHD) is proved conducive to improving the predictive capability of our model. The SPPRS is applied to seven benchmark test functions and a complex engineering problem. The results illustrate the promising benefits of this novel surrogate modeling technique.

A CAD/CAE incorporate software framework using a unified representation architecture

An incorporate CAD/CAE software framework for structural design is proposed.A unified representation architecture is presented.Design and analysis information use the same data structure.CAD model display and CAE post-processor shares the unified mesh data.The comparison of two case studies from simple to complex is presented. Currently, there are still some big gaps between the CAD system and CAE system, e.g. the different data structure for model representation, which costs lots of time and effort of engineers in the interaction between these two kinds of systems. In order to bridge these gaps, an incorporate software framework is proposed in this paper. In this framework, the unified representation architecture (URA) is presented that makes CAD and CAE to be an organic entity. The URA contains three components: (1) unified data model (UDD) including unified B-rep, unified feature and unified mesh; (2) unified data management (UDM) consisting of unified interaction, unified data structure, unified Constructive Solid Geometry (CSG) history and unified interface; (3) unified display and post-processor (UDP) for both design and performance analysis. The URA facilitates the incorporation by explicitly representing design and analysis information as design features, which maintains their associations through the history chain. Besides the URA, a unified mesh data (UMD) is proposed to unify the mesh of CAD model display and CAE analysis with the purpose of reducing the redundancy of mesh data. The unified mesh data (UMD) is proposed to unify the mesh of CAD model display and CAE analysis, which greatly reduces the redundancy of mesh generation data. Finally, the high efficiency of the proposed framework is demonstrated by engineering examples.

Acceleration of free-vibrations analysis with the Dual Reciprocity BEM based on ℋ-matrices and CUDA

Purpose – The purpose of this paper is to present a novel strategy used for acceleration of free-vibration analysis, in which the hierarchical matrices structure and Compute Unified Device Architecture (CUDA) platform is applied to improve the performance of the traditional dual reciprocity boundary element method (DRBEM). Design/methodology/approach – The DRBEM is applied in forming integral equation to reduce complexity. In the procedure of optimization computation, ℋ-Matrices are introduced by applying adaptive cross-approximation method. At the same time, this paper proposes a high-efficiency parallel algorithm using CUDA and the counterpart of the serial effective algorithm in ℋ-Matrices for inverse arithmetic operation. Findings – The analysis for free-vibration could achieve impressive time and space efficiency by introducing hierarchical matrices technique. Although the serial algorithm based on ℋ-Matrices could obtain fair performance for complex inversion operation, the CUDA parallel algorithm w...

PARALLEL STRATEGY OF FMBEM FOR 3D ELASTOSTATICS AND ITS GPU IMPLEMENTATION USING CUDA

Finite Element Method (FEM1) is pervasively used in most of 3D product design analysis, in which Computer Aided Design (CAD) models need to be converted in to mesh models first and then enriched with some material features and boundary conditions data, etc. The interaction between CAD models and FEM models is intensive. Boundary Element Method (BEM) has been expected to be advantageous in large-scale problems in recent years owing to its reduction of the dimensionality and its reduced complexity in mesh generation. However, the BEM application has so far been limited to relatively small problems due to the memory and computational complexity for matrix buildup are O(N2). The fast multipole BEM (FMBEM) combined with BEM and fast multipole method (FMM) can overcome the defect of the traditional BEM, and provides an effective method to solve the large-scale problem. Combining GPU parallel computing with FMBEM can further improve its efficiency significantly. Based on the three-dimensional elastic mechanics problems, the parallelisms of the multipole moment (ME), multipole moment to multipole moment (M2M) translation, multipole moment to local expansion (M2L) translation, local expansion to local expansion (L2L) translation and near-field direct calculation were analyzed respectively according to the characteristics of the FMM, and the parallel strategies under CUDA were presented in this paper. Three main major parts are included herein: (1) FMBEM theory in 3D elastostatics, (2) the parallel FMBEM algorithm using CUDA, and (3) comparison the GPU parallel FMBEM with BEM, FEM and FMBEM respectively by engineering examples. Numerical example results show the 3D elastostatics GPU FMBEM not only can speed up the boundary element calculation process, but also save memory which can be effective to solve the large-scale engineering problems.Copyright

M2L optimization in FMBEM and its GPU implementation

The translation from multipole moments to local moments (M2L) in the fast multipole boundary element method (FMBEM) costs too much time; we compare three methods of M2L optimization from the three following aspects: accuracy, efficiency and memory usage with an engineering numerical example, and then present a GPU parallel algorithm using CUDA for one of the front three methods which transfers child cell’s coefficients to their father cell, meanwhile, improve the tree structure by redefining the whole cells in different levels which can avoid writing data conflict in the parallel strategy. Finally, we use the threedimensional elastic BEM problems of chassis parts to verify the algorithm, and the result shows that the accelerating effect of this method is significant.

A New Approach to Generic Design Feature Recognition by Detecting the Hint of Topology Variation

Current design feature recognition mainly depends on the connective attributes of edges or faces in the CAD models, such as convexity, concavity, and tangency. However, it is difficult to uniquely define the mixed connective attributes of the generic features in some cases. A novel generic design feature recognition approach by detecting the hint of topology variation is presented in this study. The core idea includes: 1) the resulting CAD model of a complex part is regarded as formed from an initial basic shape such as roughcast and has been operated by introducing generic design features, which subsequently may cause topology variation; 2) Such topology variations, e.g. vertex elimination, edge partition and face alteration, are utilized to obtain generalized properties of the generic design features, dispensing with the connective attributes.Finally, 1) we demonstrate in the experiments that the approach successfully recognizes the main types of generic design features, both isolate and hybrid features. 2) Furthermore, we exhibit the application of the approach in some engineering examples.Copyright

Boundary Condition Related Mixed Boundary Element and its Application in FMBEM for 3D Elastostatic Problem

A boundary condition (BC) related mixed element method is presented to address the corner problem in boundary element method (BEM) for 3D elastostatic problems. In this method, noncontinuous elements (NCEs) are only used at the displacement-prescribed corners/edges and continuous elements (CEs) in other places, which can decrease the degrees of freedom (DOFs) compared to the approach using NCEs at all corners/edges. Moreover, an automatic generation algorithm of BC related mixed linear triangular elements is implemented with the help of 3D modeling engine ACIS, and the boundary element analysis (BEA) is integrated into CAD systems. In order to solve large scale problems, the fast multipole BEM (FMBEM) with mixed elements is proposed and utilized in the BEA. The examples show that the node shift scheme adopting 1/4 is optimal and the BEM/FMBEM using mixed elements can produce more accurate results by only increasing a small number of DOFs.

Integrating multiple sensors for the closed-loop three-dimensional digitization

In this article, we present a set of novel techniques, which include (1) sensor-stage calibration, (2) high-level script programming for the flexible control of data sensing, and (3) a framework for dynamic data sensing, visualization and shape modeling. It enables the integration of multiple three-dimensional sensors into one controlled three-dimensional digitization system for the closed-loop of data sensing and shape modeling. In this system, point, line, and area sensors with different sensing coverage, accuracies, and resolutions can be integrated into a multi-stage platform on which data acquisition from each sensor can be programmed in a controlled manner. In this manner, the closed-loop of data sensing and shape modeling can be achieved, which can significantly improve the overall digitization efficiency and shape modeling quality. Finally, two three-dimensional digitization examples of such multi-sensor system are demonstrated, (1) complementary integration of multiple sensors for three-dimensional digitization and (2) the closed-loop of dynamic data sensing and shape modeling to significantly improve overall sensing efficiency and shape modeling quality.

Acceleration of Modal Analysis by FMM Based on DRBEM

This paper proposes a novel algorithm to accelerate the process of modal analysis in 3D elastodynamic problems in BEM (boundary element method) with high accuracy. Because of low efficiency and high cost, conventional BEM is rarely used for solving 3D elastodynamics problems in engineering problems. With applying the DRBEM (dual reciprocity boundary element method) to form new integral equations of 3D elastodynamics problems to reduce time complexity by using reciprocity method twice, we introduce modified FMM (fast multipole method) to simplify the computation process and improve the efficiency from O(n2) to O(n) in matrix multiplication. The main features in this method are: (1) Position Location (PL) algorithm is used to eliminate one layer of nested loops in conventional FMM, and which achieve a good performance in efficiency; (2) time dimension integrations in the element of matrices are canceled for high efficiency; (3) instead of the interaction between points, we apply point to element interaction method for saving plenty of the CPU cost in modified FMM; (4) it does not need to compute complex dynamic fundamental solutions which are necessary in conventional BEM. In this algorithm, the corresponding eigenvalue problem is solved by Hessenberg matrix and QR reduction algorithm iteratively. We have tested our method in numerical examples during last section, and have observed significant optimal results in efficiency and accuracy.Copyright