Peter Arbenz


Last Name

Arbenz

First Name

Peter

ORCID

0000-0002-1501-3176

Organisational unit

Filters

Reset filters

Search Results

Publications1 - 10 of 16
  • Batched transpose-free ADI-type preconditioners for a Poisson solver on GPGPUs
    Item type: Journal Article
    Arbenz, Peter; Říha, Lubomír (2020)
    Journal of Parallel and Distributed Computing
  • Special issue on Parallel Matrix Algorithms and Applications (PMAA’10)
    Item type: Other Journal Item
    Arbenz, Peter; Saad, Yousef; Sameh, Ahmed; et al. (2011)
    Parallel Computing
  • Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems
    Item type: Conference Paper
    Arbenz, Peter; Geus, Roman (2005)
    Applied Numerical Mathematics
    We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the Jacobi–Davidson algorithm and of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. We present numerical results of very large eigenvalue problems originating from the design of resonant cavities of particle accelerators.
  • Comparison of Parallel Time-Periodic Navier-Stokes Solvers
    Item type: Conference Paper
    Arbenz, Peter; Hupp, Daniel; Obrist, Dominik (2018)
    Lecture Notes in Computer Science ~ Parallel Processing and Applied Mathematics 12th International Conference, PPAM 2017, Lublin, Poland, September 10-13, 2017, Revised Selected Papers, Part I
  • A Parallel Multigrid Solver for Time-Periodic Incompressible Navier–Stokes Equations in 3D
    Item type: Conference Paper
    Benedusi, Pietro; Hupp, Daniel; Arbenz, Peter; et al. (2016)
    Lecture Notes in Computational Science and Engineering ~ Numerical Mathematics and Advanced Applications ENUMATH 2015
  • Multi-level preconditioning and eigenvector approximation for axisymmetric Maxwell eigenproblems
    Item type: Conference Paper
    Kranjčević, Marija; Arbenz, Peter; Adelmann, Andreas (2018)
    Proceedings in Applied Mathematics and Mechanics
  • Microstructural Finite Element Analysis of Human Bone Structures
    Item type: Journal Article
    Arbenz, Peter; Müller, Ralph (2008)
    ERCIM News
  • A scalable multi-level preconditioner for matrix-free µ-finite element analysis of human bone structures
    Item type: Journal Article
    Arbenz, Peter; van Lenthe, G. Harry; Mennel, Uche; et al. (2008)
    International Journal for Numerical Methods in Engineering
    The recent advances in microarchitectural bone imaging disclose the possibility to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. Coupling these imaging possibilities with microstructural finite element (µFE) analysis offers a powerful tool to improve bone stiffness and strength assessment for individual fracture risk prediction. Many elements are needed to accurately represent the intricate microarchitectural structure of bone; hence, the resulting µFE models possess a very large number of degrees of freedom. In order to be solved quickly and reliably on state-of-the-art parallel computers, the µFE analyses require advanced solution techniques. In this paper, we investigate the solution of the resulting systems of linear equations by the conjugate gradient algorithm, preconditioned by aggregation-based multigrid methods. We introduce a variant of the preconditioner that does not need assembling the system matrix but uses element-by-element techniques to build the multilevel hierarchy. The preconditioner exploits the voxel approach that is common in bone structure analysis, and it has modest memory requirements, at the same time robust and scalable. Using the proposed methods, we have solved in 12min a model of trabecular bone composed of 247 734 272 elements, yielding a matrix with 1 178 736 360 rows, using 1024 CRAY XT3 processors. The ability to solve, for the first time, large biomedical problems with over 1 billion degrees of freedom on a routine basis will help us improve our understanding of the influence of densitometric, morphological, and loading factors in the etiology of osteoporotic fractures such as commonly experienced at the hip, spine, and wrist.
  • Intrinsic Fault Tolerance of Multi Level Monte Carlo Methods
    Item type: Report
    Pauli, Stefan; Arbenz, Peter; Schwab, Christoph (2012)
    SAM Research Report
    Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to solvers for Partial Differential Equations with random input data are shown to exhibit intrinsic failure resilience. Sufficient conditions are provided for non-recoverable loss of a random fraction of samples not to fatally damage the asymptotic accuracy vs. work of an MC simulation. Specifically, the convergence behavior of MLMC methods on massively parallel hardware is analyzed mathematically and computationally, under general assumptions on the node failures and on the sample failure statistics on the different MC levels, in the absence of checkpointing, i.e. we assume irrecoverable sample failures with complete loss of data. Modifications of the MLMC with enhanced resilience are proposed. The theoretical results are obtained under general statistical models of CPU failure at runtime. Specifically, node failures with the so-called Weibull failure models on massively parallel stochastic Finite Volume computational fluid dynamics simulations are discussed.
  • Multilevel Monte Carlo for the Feynman–Kac formula for the Laplace equation
    Item type: Journal Article
    Pauli, Stefan; Gantner, Robert Nicholas; Arbenz, Peter; et al. (2015)
    BIT Numerical Mathematics
    Since its formulation in the late 1940s, the Feynman–Kac formula has proven to be an effective tool for both theoretical reformulations and practical simulations of differential equations. The link it establishes between such equations and stochastic processes can be exploited to develop Monte Carlo sampling methods that are effective, especially in high dimensions. There exist many techniques of improving standard Monte Carlo sampling methods, a relatively new development being the so-called Multilevel Monte Carlo method. This paper investigates the applicability of multilevel ideas to the stochastic representation of partial differential equations by the Feynman–Kac formula, using the Walk on Spheres algorithm to generate the required random paths. We focus on the Laplace equation, the simplest elliptic PDE, while mentioning some extension possibilities.
Publications1 - 10 of 16