Jeffrey M. Connors

Multiphysics simulations: Challenges and opportunities

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

Partitioned Time Stepping for a Parabolic Two Domain Problem

There have been many numerical simulations but few analytical results of stability and accuracy of algorithms for computational modeling of fluid-fluid and fluid-structure interaction problems, where two domains corresponding to different fluids (ocean-atmosphere) or a fluid and deformable solid (blood flow) are separated by an interface. As a simplified model of the first examples, this report considers two heat equations in

Decoupled Time Stepping Methods for Fluid-Fluid Interaction

\Omega_1,\Omega_2\subset\mathbb{R}^2

A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection

adjoined by an interface

Small-scale divergence penalization for incompressible flow problems via time relaxation

I=\Omega_1\cap\Omega_2\subset\mathbb{R}

Adjoint Error Estimation for Linear Advection

. The heat equations are coupled by a condition that allows energy to pass back and forth across the interface

Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport

I

Convergence analysis and computational testing of the finite element discretization of the Navier–Stokes alpha model

while preserving the total global energy of the monolithic, coupled problem. To compute approximate solutions to the above problem only using subdomain solvers, two first-order in time, fully discrete methods are presented. The methods consist of an implicit-explicit approach, in which the action across

On the accuracy of the finite element method plus time relaxation

I

Partitioned time discretization for parallel solution of coupled ODE systems

is lagged, and a partitioned method based on passing interface values back and forth across