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This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. As a consequence a few strategies are developed whose goal is to achieve this feature. A number of “templates” for enabling implementations of these factorizations are presented. Numerical experiments show that the resulting ILUs offer a good compromise between robustness and efficiency.

Figure 1: Quadrangulation on Rockarm model. Figure (a) shows the quasi-dual Morse-Smale complex of an unconstrained eigenfunction. Taking the direction (arrows), alignment (lines) and sizing (color) fields of figure (b) into account, our scheme computes a scalar function with the quasi-dual Morse-Smale complex shown in (c). In (d) we depict our final quadrangulation result. This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the Morse-Smale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigenproblem we can generate a scalar field on the mesh whose Morse-Smale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the Morse-Smale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.

Abstract — In probabilistic mobile robotics, the development of measurement models plays a crucial role as it directly influences the efficiency and the robustness of the robot’s performance in a great variety of tasks including localization, tracking, and map building. In this paper, we present a novel probabilistic measurement model for range finders, called Gaussian beam processes, which treats the measurement modeling task as a nonparametric Bayesian regression problem and solves it using Gaussian processes. The major benefit of our approach is its ability to generalize over entire range scans directly. This way, we can learn the distributions of range measurements for whole regions of the robot’s configuration space from only few recorded or simulated range scans. Especially in approximative approaches to state estimation like particle filtering or histogram filtering, this leads to a better approximation of the true likelihood function. Experiments on real world and synthetic data show that Gaussian beam processes combine the advantages of two popular measurement models. I.

We present an appearance-based user interface for artists to efficiently design customized image-based lighting environments. 1 Our approach avoids typical iterations of parameter editing, rendering, and confirmation by providing a set of intuitive user interfaces for directly specifying the desired appearance of the model in the scene. Then the system automatically creates the lighting environment by solving the inverse shading problem. To obtain a realistic image, all-frequency lighting is used with a spherical radial basis function (SRBF) representation. Rendering is performed using precomputed radiance transfer (PRT) to achieve a responsive speed. User experiments demonstrated the effectiveness of the proposed system compared to a previous approach. 1.

By using a combination of 32-bit and 64-bit floating point arithmetic the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. These ideas can be applied to sparse multifrontal and supernodal direct techniques and sparse iterative techniques such as Krylov subspace methods. The approach presented here can apply not only to conventional processors but also to exotic technologies such as

y work of this author was performed while he was on a sabbatical visit to NERSC.

This article explores the coupling of coarse and fine-grained parallelism for Finite Element simulations based on efficient parallel multigrid solvers. The focus lies on both system performance and a minimally invasive integration of hardware acceleration into an existing software package, requiring no changes to application code. Because of their excellent price performance ratio, we demonstrate the viability of our approach by using commodity graphics processors (GPUs) as efficient multigrid preconditioners. We address the issue of limited precision on GPUs by applying a mixed precision, iterative refinement technique. Other restrictions are also handled by a close interplay between the GPU and CPU. From a software perspective, we integrate the GPU solvers into the existing MPI-based Finite Element package by implementing the same interfaces as the CPU solvers, so that for the application programmer they are easily interchangeable. Our results show that we do not compromise any software functionality and gain speedups of two and more for large problems. Equipped with this additional option of hardware acceleration we compare different choices in increasing the performance of a conventional, commodity based cluster by increasing the number

SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase preeliminates singletons by permuting the input matrix into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill-reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of A T A. Rank-detection is performed within each frontal matrix using Heath’s method, which does not require column pivoting. The resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.

This paper describes an open framework that enables the online utilization and the collaborative development of structural analysis programs (Peng and Law 2000, Peng et al. 2000)