A polyvalent C++ and Python FEM library.

Summary: We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. It support static and dynamic problems, and differentiation with respect to all physical parameters involved, including shape, elastic parameters, friction coefficient, and initial conditions. Our analytically derived adjoint formulation is over 10x faster than automatic differentiation. code.

Summary: Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. We adapt this approach to complex shapes in situations when preserving the shape's surface is important. We propose an automated and robust pipeline based on this approach with the ability of handling 2D and 3D shapes of high complexity.

Summary: We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated solutions for evaluation of numerical schemes for incompressible Navier-Stokes equations in laminar flow regime. We compare the performance of a representative selection of most broadly used algorithms for Navier-Stokes equations on this set of problems.

Honors Analysis of Algorithms, 2023
Honors Analysis of Algorithms, 2022
Computer Graphics, 2021

Numerical Linear Algebra, 2019
Multivariate Calculus, 2018