Abstract not found

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.

In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several right-hand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have

A dynamic simulation method for multi-body systems is presented in this paper. The special feature of this method is that it satisfies all given constraints by computing impulses. In each simulation step the joint states after the step are predicted. In order to obtain valid states after the simulation step, impulses are computed and applied to the connected bodies. Since a valid joint state is targeted exactly, there is no drift as the simulation proceeds in time and so no additional stabilisation is required. In previous approaches the impulses for a multi-body system were computed iteratively. Since dependencies between joints were not taken into account, the simulation of complex models was slow. A novel method is presented that uses a system of linear equations to describe these dependencies. By solving this typically sparse system the required impulses are determined. This method allows a very fast simulation of complex multi-body systems. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation 1.

We propose a framework for 3D geometry processing that provides direct access to surface curvature to facilitate advanced shape editing, filtering, and synthesis algorithms. The central idea is to map a given surface to the curvature domain by evaluating its principle curvatures, apply filtering and editing operations to the curvature distribution, and reconstruct the resulting surface using an optimization approach. Our system allows the user to prescribe arbitrary principle curvature values anywhere on the surface. The optimization solves a nonlinear least-squares problem to find the surface that best matches the desired target curvatures while preserving important properties of the original shape. We demonstrate the effectiveness of this processing metaphor with several applications, including anisotropic smoothing, feature enhancement, and multi-scale curvature editing.

This paper presents an efficient simulation method for parallel cloth simulation. The presented method uses an impulse-based approach for the simulation. Cloth simulation has many application areas like computer animation, computer games or virtual reality. Simulation methods often make the assumption that cloth is an elastic material. In this way the simulation can be performed very efficiently by using spring forces. These methods disregard the fact that many textiles cannot be stretched significantly. The simulation of inextensible textiles with methods based on spring forces leads to stiff differential equations which cause a loss of performance. In contrast to that, in this paper a method is presented that simulates cloth by using impulses. The mesh of a cloth model is subdivided into strips of constraints. The impulses for each strip can be computed in linear time. The strips that have no common particle are independent from each other and can be solved in parallel. The impulse-based method allows the realistic simulation of inextensible textiles in real-time. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation 1.

In this article, we present several new permutations for I-matrices making these more suitable for incomplete LDU-factorization preconditioners used in solving linear systems by iterative methods. A general matrix can be transformed by row permutation as well as row and columns scaling into an I-matrix, i.e. a matrix having elements of modulus 1 on the diagonal and elements of modulus of no more than 1 elsewhere. Reordering rows and columns by the same permutation clearly preserves I-matrices. In this article, we consider such reordering techniques which make the permuted matrix more suitable for an incomplete LDU-factorization preconditioner than the original I-matrix. We use a multilevel ILUC, an incomplete LDU-factorization preconditioner using Crout’s implementation of Gaussian elimination without pivoting to test these reorderings. The combination of I-matrix preprocessing with the various algorithms presented here and the multilevel incomplete LDU-factorizations forms a powerful preconditioning method for unsymmetric, highly indefinite problems.

Abstract Soft-field imaging methods, such as Optical Tomography (OT) and Electrical Impedance Tomography (EIT) have significant potential for medical imaging as they are non-invasive, portable and inexpensive. Possible clinical applications include epilepsy monitoring, cerebral stroke differentiation and screening for breast cancer. Recent advances in data acquisition instrumentation and image reconstruction algorithms raise the requirement to handle multiple large datasets from detailed large-scale geometric descriptions of biological objects. Thus, a major bottleneck lies in processing a large number of linear equations that result from the Finite-Element formulation of soft-field problems. Common numerical tools are not suited for large-scale problems, therefore alternative approaches are required. We propose the facilitation of an innovative multi-level inverse-based incomplete LU preconditioning approach to improve computational efficiency in processing EIT and OT system matrices. This combines static reordering and scaling, controlled growth of the inverse of triangular factors, and approximation of the Schur-complement in a multi-level scheme. Comparison with conventional incomplete LU factorisation provided a speed improvement of up to 11 times in preconditioner setup time, and up to 12 times in solution runtime for large-scale models. In addition, a new approach of monopolar current sources is introduced. Current sources and sinks are represented by linear combinations of a compact monopolar sources basis. Only the corresponding monopolar solutions are processed. These solutions serve as a basis for construction of the entire excitation pattern. This approach exploits the information content given in the system in an optimal manner and therefore avoids redundant computation. Key Words, complex-valued, large-scale problems, soft-field, multi-level preconditioner, Krylov-subspace, monopolar sources, modelling, EIT, DOT, high order radiation transfer

Abstract not found

Efficient methods for solving linear-programming problems in exact precision rely on the solution of sparse systems of linear equations over the rational numbers. We consider a test set of instances arising from exact-precision linear programming and use this test set to compare the performance of several techniques designed for symbolic sparse linear-system solving. We compare a direct exact solver based on LU factorization, Wiedemann’s method for black-box linear algebra, Dixon’s p-adic-lifting algorithm, and the use of iterative numerical methods and rational reconstruction as developed by Wan.