The faculty and students at SUNY Polytechnic Institute have been actively contributing to the field of Geometric Mechanics and Structure-Preserving Discretizations, presenting their research at prestigious international conferences and workshops. Their work highlights cutting-edge methods in applied mathematics and computational mechanics that have significant implications for engineering, physics, and material science. Below are some recent accomplishments by SUNY Poly’s talented faculty and students.
Dr. Dziubek’s Talk at SNP2024
Dr. Andrea Dziubek, Applied Mathematics Professor, delivered a round table talk titled “Intrinsic Mixed Finite Element Methods for Linear Cosserat Elasticity,” at the 58th Meeting of the Society for Natural Philosophy (SNP2024) in Aarhus, Denmark, on June 12, 2024.
Her joint work with Michael Karow, Kaibo Hu, and Michael Neunteufel explores advanced numerical methods for modeling materials with micropolar structure, where each point acts like a rigid body with both translational and rotational degrees of freedom.
In her presentation, Dziubek discussed finite element exterior calculus (FEEC), a robust framework for designing numerical methods to solve partial differential equations. Specifically, the talk examined how the Cosserat elasticity model can be viewed as a Hodge-Laplacian problem and how the coupling constant between displacement and microrotation can lead to computational challenges such as locking. Dziubek and her collaborators proposed locking-free finite element discretization methods that could overcome these issues, making this work highly relevant to researchers in materials science and applied mathematics.
Nicholas Andrzejkiewicz Presents at WCCM24
Nicholas Andrzejkiewicz, a 2024 graduate with a BS in Mathematics, presented a poster titled “Geometry and Topology in New Numerical Methods for Electromagnetism and Continua.” at the 16th World Congress on Computational Mechanics (WCCM24) in July 2024. His poster focused on the application of differential forms and geometric quantities in finite element methods, which offer structure-preserving properties that traditional methods lack.
The poster emphasized how finite element methods based on differential forms provide stability and preserve the geometric properties of physical systems, such as electromagnetism and continuum mechanics. This work is part of a broader trend in computational mechanics that seeks to maintain the fundamental structure of physical laws, even when they are discretized for numerical solutions. Andrzejkiewicz’s research is a testament to the strong foundation in both geometry and physics that SUNY Poly students gain through their studies.
Chawn Neal’s Presents Research at SURP
Chawn Neal, a double major in Computer Science and Mathematics, presented his research poster titled “A Glance at Finite Element Analysis and Exterior Calculus” at the SUNY Poly Undergraduate Research Program (SURP) on August 2, 2024. His work delved into the Finite Element Exterior Calculus (FEEC) method, which is widely used to solve partial differential equations in complex domains while preserving critical quantities from the continuous problem.
Neal’s research specifically addressed the Hodge-Laplace eigenvalue problem using mixed methods within the FEEC framework. The poster also outlined his use of NGSolve, a Python-based high-performance Multiphysics software, to implement his solutions. His exploration of advanced mathematical theories like Stokes’ theorem, Hodge theory, and homological algebra demonstrates the breadth of knowledge Neal has applied to his research.
Dr. Dziubek at SIAM AN 2024
Andrea Dziubek also attended the Society for Industrial and Applied Mathematics Annual Meeting (SIAM AN 24) held in Spokane, Washington, in July 2024. During the sessions on Numerical Methods for Geometric PDEs, Dziubek met with collaborators and participated in discussions that furthered her research in applied mathematics. These sessions focused on computational approaches to solving partial differential equations (PDEs) that arise in geometric contexts, further reinforcing SUNY Poly’s involvement in advancing these critical mathematical methods.
These recent accomplishments of SUNY Poly faculty and students in the field of Geometric Mechanics and Structure-Preserving Discretizations showcase their commitment to cutting-edge research in applied mathematics. From advanced finite element methods to novel applications in electromagnetism and material science, SUNY Poly is making significant strides in this complex field, contributing to the broader scientific community through presentations at international conferences and meetings.