CAM Colloquium: Short Research Presentations by Assistant Professors Anil Damle (CS), Mahdi Esmaily Moghadam (MAE), and Nikolaos Bouklas (MAE)

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Anil Damle, Assistant Professor, CS Invariant subspace perturbation theory and applications There are many classical results that allow us to understand how invariant subspaces of a matrix behave with respect to perturbations of that matrix. However, they often capture changes in invariant subspaces with respect to the spectral or Frobenius norm whereas many modern applications require control of such perturbations with respect to "row-wise" norms (such as the two-to-infinity matrix norm). For example, many algorithms for spectral clustering are either directly motivated by or may be analyzed by understanding properties of invariant subspaces. In this talk we briefly discuss new deterministic bounds on how invariant subspaces change with respect to the two-to-infinity norm as a result of perturbations to the underlying matrix. In particular, understanding in what ways our bounds are tight deterministically makes them an ideal starting point for the analysis of specific algorithms and applications (particularly for random models). Mahdi Esmaily Moghadam, Assistant Professor, MAE Inherently parallel linear solver for CFD Computational fluid dynamics (CFD) is used extensively for analyzing fluid flows in complex domains and improving engineering designs. One of the obstacles to the broader adoption of CFD is the cost of the solution particularly in problems involving complex geometries with high aspect ratio, higher Reynolds number flows, multi-domain simulations, fluid-structure interaction, and optimization among others. The cost of CFD simulations primarily stems from the underlying linear solver, underscoring the need for more efficient iterative solvers. Thus, in this talk, I will motivate the development of a new generation of linear solvers for CFD problems that are inherently parallel. The main idea of the new approach is to exploit extra calculations that are performed in a parallel implementation (originally for consistency of a parallel and sequential implementation) in order to improve the convergence rate of the iterative solver. If successful, this new approach has far-reaching implications as it can improve scalability and reduce the cost of massively parallel calculations performed on large clusters. Nikolaos Bouklas, Assistant Professor, MAE Research in computational solid mechanics of soft, active and biological materials This short talk will include an overview of the ongoing research focus in the area of computational solid mechanics, multi-physics and multi-scale simulation in Prof. Bouklas’ group. Starting from fundamentals in theoretical and applied mechanics and an inherent interest in soft, active and biological materials, as well as fracture, instabilities and constitutive modeling, several topics are studied. Multiphysics of solid-fluid aggregates are studied focusing on the coupled response of the systems and the development of stabilized mixed-finite element schemes. Gradient damage modeling for the study of fracture in elastomers with chain length distributions, and in the cases where surface stresses are present. Phase-field modeling for strain-induced crystallization in elastomers. Multiscale schemes for the study of polymer networks including the use of learning schemes for the speed-up of the computations. Development of extended symmetric Galerkin boundary element methods (XSGBEM) for fracture mechanics calculations. Stability analysis, localization and loss of ellipticity in soft composites, along with numerical homogenization schemes. Use of phase field modeling for brittle fracture and XSGBEM for the study of environmentally assisted fractures and hydraulic fracturing for subsurface modeling. Both open source and in-house codes are used in an HPC setting for the study of these problems.