A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-0

Extranoematic artifacts: neural systems in space and topology

During the past several decades, the evolution in architecture and engineering went through several stages of exploration of form. While the procedures of generating the form have varied from using physical analogous form-finding computation to engaging the form with simulated dynamic forces in digital environment, the self-generation and organization of form has always been the goal. this thesis further intend to contribute to self-organizational capacity in Architecture. The subject of investigation is the rationalizing of geometry from an unorganized point cloud by using learning neural networks. Furthermore, the focus is oriented upon aspects of efficient construction of generated topology. Neural network is connected with constraining properties, which adjust the members of the topology into predefined number of sizes while minimizing the error of deviation from the original form. The resulted algorithm is applied in several different scenarios of construction, highlighting the possibilities and versatility of this method

A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our existing single-GPU hierarchical matrix library hmglib such that it is able to scale on many GPUs and such that it can be coupled to arbitrary application codes. Using a model GPU implementation of a boundary element method (BEM) solver, we are able to achieve more than 67 percent relative parallel speed-up going from 128 to 1024 GPUs for a model geometry test case with 1.5 million unknowns and a real-world geometry test case with almost 1.2 million unknowns. On 1024 GPUs of the cluster Titan, it takes less than 6 minutes to solve the 1.5 million unknowns problem, with 5.7 minutes for the setup phase and 20 seconds for the iterative solver. To the best of the authors' knowledge, we here discuss the first fully GPU-based distributed-memory parallel hierarchical matrix Open Source library using the traditional H-matrix format and adaptive cross approximation with an application to BEM problems

Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension

In this paper we present various distributed algorithms for LP-type problems in the well-known gossip model. LP-type problems include many important classes of problems such as (integer) linear programming, geometric problems like smallest enclosing ball and polytope distance, and set problems like hitting set and set cover. In the gossip model, a node can only push information to or pull information from nodes chosen uniformly at random. Protocols for the gossip model are usually very practical due to their fast convergence, their simplicity, and their stability under stress and disruptions. Our algorithms are very efficient (logarithmic rounds or better with just polylogarithmic communication work per node per round) whenever the combinatorial dimension of the given LP-type problem is constant, even if the size of the given LP-type problem is polynomially large in the number of nodes