​​​​World Congress in Computational Mechanics 2018

​​​​Recent Advances in Solving Stiff Phenomena in Computation Mechanics

​​​​Dominik L. Michels · Mayya Tokman · David E. Keyes

​​​​Jul. 22-27, 2018, Times Square, New York City, US-NY

Congress Overview

The thirteenth World Congress in Computational Mechanics (WCCM XIII) is expected to be one of the most attended, and most broadly themed gatherings of applied mathematicians, computational scientists, and engineers working on areas related to computational physics, material sciences, finite element analysis, design and optimization, structural mechanics, fluid mechanics, and inverse problems. Participants from all parts of the globe represent multiple sectors, including academia, government, and industry. It will be co-located with the second Pan American Congress on Computational Mechanics (PANACM II).

Our symposium on recent advances in solving stiff phenomena in computation mechanics (No. 801) as part of the WCCM XIII will highlight selected outstanding work providing an overview on recent developments in this regard bringing together theorist and practitioners.

Goals and Objectives

For most problems, simulating dynamics more accurately invariably means sacrificing computational efficiency. This is especially the case, when the underlying differential equations are stiff. Such systems of equations are characterized by a wide range of time scales present in their evolution. Stiffness arises when the time scale of interest in the dynamics is much slower than the fastest modes of the system. Stiff equations are ubiquitous in a wide range of fields including computational mechanics. Prominent examples include the dynamics of cloth, fibers, fluids, or solids, and their interaction with each other including collision and (frictional) contact handling.

The numerical time integration of stiff systems of differential equations is one of the central problems in numerical analysis. The history of this branch of numerical analysis has been dominated by two classes of time integrators: explicit and implicit. Both types of integrators allow advancing the numerical solution along a discretized time interval, but the numerical properties of these two classes are fundamentally different. Explicit methods require the least amount of computations per time step but suffer severe stability restrictions that limit the allowable size of the time step. Implicit methods possess better stability properties and allow for accurate integration with a much larger time step, but the increase in time step size comes at the expense of significantly more computations required in each time iteration. As the stiffness of the problem grows, integrating equations explicitly over a long period of time becomes impractical and modelers turn to implicit methods. However, implicit schemes are not immune to the increase in stiffness and the amount of computation required per time step grows correspondingly.

Recently, exponential methods emerged as a viable alternative to implicit schemes for a number of stiff problems. A range of exponential integrators have been developed including stiffly accurate methods that are particularly suited for the integration of stiff systems. Moreover, significant progress has been achieved in the development of modern Krylov subspace projection methods.

In this workshop, we intend to discuss recent developments in solving stiff differential equations as state-of-the-art exponential integrators and modern Krylov subspace projection methods. This is tailored to the particular needs of applications in computational mechanics.

Talks (in alphabetical order by presenting author)

  1. Partitioned Adaptive Parallel Multirate Methods for Coupled Stiff Systems.

    Philipp Birken (presenting), Lund University,
    Peter Meisrimel, Lund University,
    Azahar Monge, Lund University.

  2. Constructing New Time Integrators Using Interpolating Polynomials.

    Tommaso Buvoli, University Of Washington.

  3. Application of Exponential Time Integration Methods in Numerical Weather Prediction Models.

    Stéphane Gaudreault (presenting), Environment and Climate Change Canada,
    Michel Desgagné, Environment and Climate Change Canada,
    Greg Rainwater, California State University, Monterey Bay,
    Valentin Dallerit, University of California Merced,
    Mayya Tokman, University of California Merced.

  4. Parallel Adaptive Implicit Extrapolation Methods.

    David Ketcheson, KAUST.

  5. Instability Problems of Implicit FEM Solution Procedures for Fast Rotating Structures - Instability Sources and Solutions.

    Markus Kober (presenting), Brandenburg University of Technology,
    Arnold Kühhorn, Brandenburg University of Technology,
    Akin Keskin, Rolls-Royce plc.

  6. Symbolic-Numeric Methods for Solving Differential Equations in Scientific Computing.

    Dmitry Lyakhov, KAUST.

  7. Exponential Integrators.

    Alexander Ostermann (keynote), University of Innsbruck.

  8. Structure-preserving Numerical Integrators for Relaxation Oscillators, with Application to Neuronal Dynamics.

    Ari Stern, Washington University in St. Louis.

  9. Exponential Integrators: Methods and Software.

    Mayya Tokman, University of California Merced.

  10. Evaluation of Implicit-Explicit, Additive Runge-Kutta Method Efficiency in Simulating Global Non-Hydrostatic Atmospheric Dynamics for Earth System Modeling.

    Christopher Vogl (presenting), Lawrence Livermore National Laboratory,
    David Gardner, Lawrence Livermore National Laboratory,
    Daniel Reynolds, Southern Methodist University,
    Paul Ullrich, University of California Davis,
    Carol Woodward, Lawrence Livermore National Laboratory,
    Andrew Steyer, Sandia National Laboratories.

  11. A Generalized Algorithm for Finite Strain Plasticity.

    Alfio Grillo, Politecnico Torino,
    Raphael Prohl, G-CSC Frankfurt University,
    Gabriel Wittum (presenting), KAUST.

  12. Application of Hamiltonian Flows to Exploring Parameters of Mathematical Models in Situations with Insufficient Data.

    Mizuka Komatsu, Kobe University,
    Takaharu Yaguchi (presenting), Kobe University / JST PRESTO.

Schedule & Registration

The symposium as part of the World Congress on Computational Mechanics will take place on July 25 from 2:00PM to 6:30PM and July 26 from 9:45AM to 4:00PM in Room #Harlem at Marriott Marquis-7, Times Square, New York City, US-NY.

Presenting authors have to register by April 30 for the upcoming World Congress on Computational Mechanics in order to ensure inclusion in the final program.