Abstract : Numerical modeling and algorithms are fundamental building blocks in computational science and engineering that provide accurate and efficient solution methods to the model equations. As applications become more complex, the model equations become more difficult and sophisticated. New and efficient numerical techniques are hence needed to solving the physical equations. The goal of this mini-symposium is to present the recent developments of computational methods for applications. The topics include numerical methods for PDEs, fast solvers, adaptive methods, and software developments. The mini-symposium will emphasize both the design and analysis of numerical algorithms as well as applications in science and engineering.
[02041] Numerical Methods for PDEs and Mesh Generation
Format : Talk at Waseda University
Author(s) :
Justin Wan (University of Waterloo)
Connor Tannahill (University of Waterloo)
Abstract : We will start with an overview of the mini-symposium. Then, in this talk, we will present a novel optimization-based approach for variational mesh adaptation based on MMPDE methods, combined with recent techniques for solving large-scale nonlinear constraint problems in parallel. The resulting method resembles meshing algorithms based on the spring analogy while producing high-quality adaptive meshes. We demonstrate the advantages of our method over standard MMPDE methods for generating two and three-dimensional meshes in parallel.
[01595] PDAEs redux
Format : Talk at Waseda University
Author(s) :
Uri Michael Ascher (University of BC)
Abstract : We re-examine computational principles for solving constrained PDEs in large applications.
One involves simulation of friction and contact effects in deformable object motion arising in graphics and robotics.
The need to flexibly engage such constraints in differentiable models prompts introducing penalty methods,
despite some additional complexity and minor potential instability.
The other project investigates, in the context of neural ODEs,
different stabilization methods for differential equations with invariants arising from elimination of algebraic constraints.
Ronald Haynes (Memorial University of Newfoundland)
Steven Ruuth (Simon Fraser University)
Abstract : We consider the convergence of optimized Schwarz iterations for the surface intrinsic positive Helmholtz equation $(c−∆_S)u=f, c>0$, for smooth, simple closed 1-manifolds where periodicity is inherent in the geometry. We prove convergence results for the unequal-sized subdomain case with an arbitrary number of subdomains, and find an explicit formula for the optimal Robin parameter. Connections to a particular discretization, the closest point method, are provided as are numerical experiments verifying our results.
[02719] DD approaches for surface PDEs solved by the closest point method
Format : Online Talk on Zoom
Author(s) :
Ronald Haynes (Memorial University of Newfoundland and Labrador)
Abstract : The solution of surface intrinsic PDEs using the closest point method will be proposed. For efficiency we have designed and analyzed domain decomposition solvers and preconditioners to solve the resulting discrete system of equations. Numerical results for model test examples will be presented.
[02811] TVD property of second order method for two-dimensional scalar conservation laws
Format : Talk at Waseda University
Author(s) :
Lilia Krivodonova (University of Waterloo)
Alexey Smirnov (University of Waterloo)
Abstract : The total variation diminishing (TVD) property plays a crucial role in ensuring the stability and convergence of numerical solutions for one-dimensional scalar conservation laws. It was established in 1985 that in the two-dimensional space, a TVD method can be at most first order accurate. We consider a new definition of TV and propose a condition on scheme coefficients for a second-order method to be TVD for nonlinear scalar conservation laws.
[02206] Using Adaptive Time-Steppers to Explore Stability Domains
Format : Talk at Waseda University
Author(s) :
Mary Pugh (University of Toronto)
Abstract : Stability domains for ODE time-steppers are well-understood when the linearized system is diagonalizable. I'll discuss an implicit-explicit time-stepper for which the linearized system isn't diagonalizable. An adaptive time-stepper can be used to explore the stability domain. I'll present a system whose stability domain has a discontinuous boundary; a small change in a parameter can cause a jump in the time-step-size stability threshold. This is joint work with my former PhD student, Dave Yan.
[02320] Extended Statistical Modelling and Advanced Computational Approaches for Disperse Multiphase Flows
Format : Talk at Waseda University
Author(s) :
Lucian Ivan (Canadian Nuclear Laboratories)
Benoit Allard (University of Ottawa)
Francois Forgues (Canadian Nuclear Laboratories)
James McDonald (University of Ottawa)
Abstract : This talk presents an Eulerian-based polydisperse Gaussian-moment model (PGM) family for the description of particle-laden multiphase flows. The modelling approach leads to a set of first-order, robustly-hyperbolic balance laws that provide a direct treatment for local higher-order statistics, such as covariances between particle distinguishable properties (e.g., diameter, temperature, etc.) and particle velocity. A massively parallel discontinuous-Galerkin-Hancock framework is employed to efficiently obtain computational PGM-solutions for a range of flows, including bio-aerosol dispersion and fuel sprays.
[02260] tost.II: A temporal operator splitting template library for deal.II
Format : Talk at Waseda University
Author(s) :
Raymond Spiteri (University of Saskatchewan)
Kevin Green (University of Saskatchewan)
Abstract : Operator splitting is a popular and often necessary means for solving
PDEs. Software that implements operator splitting, however, generally
only allows specific splitting methods, with only specific
sub-integrators, and only for specific problems. In this talk, I
describe the tost.II temporal operator splitting library built on the
deal.II finite-element library. tost.II enables easy experimentation
with splittings for an arbitrary number of operators and with
arbitrary order of convergence, including methods with negative or
complex coefficients.
