Mathematical Models and Numerical Methods for Multiphysics Systems

May 1-3, 2024, O'Hara Student Center, University of Pittsburgh

The conference aims to bring together experts from different communities in which computational models for multiphysics systems are employed. Multiphysics systems model the physical interactions between two or more media, such as couplings of fluid flows, rigid or deformable porous media, and elastic structures. Typical examples are coupling of free fluid and porous media flows, fluid--structure interaction, and fluid--poroelastic structure interaction. Applications of interest include climate modeling, interaction of surface and subsurface hydrological systems, fluid flows through fractured or deformable aquifers or reservoirs, evolution of soil structures, arterial flows, perfusion of living tissues, and organ modeling, such as the heart, lungs, and brain. The work presented at the conference will cover both rigorous mathematical and numerical analysis and applications to cutting-edge problems.
The main topics of the conference include the following:

• Development and analysis of mathematical models for multiphysics systems. This includes developing suitable weak formulations of the PDE systems and establishing existence, uniqueness, and stability of weak solutions using techniques from nonlinear time dependent PDEs.
• Discretization methods for multiphysics systems. This includes design and analysis of structure preserving and parameter robust discretization methods, such as mixed finite element methods, discontinuous Galerkin methods, finite volume methods, mimetic finite difference methods, and virtual element methods. Of specific interest are methods that possess local mass and momentum conservation and locking-free behavior in extreme parameter regimes. Additional topics of interest include mixed-dimensional methods, a posteriori error estimation and space-time mesh adaptivity, and multiscale and reduced order models.
• Solution strategies for multiphysics systems. The complexity and large size of the resulting algebraic systems requires the development of efficient solution methods. Topics of interest include stable and higher-order loosely-coupled operator splitting and time splitting methods, domain decomposition methods, and parameter-robust monolithic solvers and preconditioners.
• Applications. These include, but are not limited to applications to the geosciences, biomedicine, and industry, such as climate modeling, interaction of surface and subsurface hydrological systems, fluid flows through fractured or deformable aquifers or reservoirs, evolution of soil structures, arterial flows, perfusion of living tissues, organ modeling, such as the eye, heart, lungs, and brain, drug delivery, LDL transport, fuel cells, and industrial filters.

Click here to register for the conference. (Registration Deadline April 15, 2024)

Program

Book of Abstracts

Conference Dinner, University Club Gold Room, May 1, 2024 at 6:00 PM:

Click here to register for the conference dinner on May 1st. For directions to the University Club from O'Hara Student Center, click here.

Hotel:

We have reserved a block of rooms at the Wyndham (Phone: (412) 682 - 6200, Click here to view the website) for the dates April 30 - May 4, 2024 at the rate of \$149 per night plus tax with an option for breakfast for \$20 per day under "Pitt Math Department Conference". Reservations can be made by calling the hotel. The cutoff date is March 31, 2024.

Click here to view the conference poster.