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Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
A strategy to construct physics-based local surrogate models for parametric Stokes flows and coupled Stokes-Darcy systems is presented. The methodology relies on the proper generalized decomposition (PGD) method to reduce the dimensionality…
We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…
An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD…
Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…
We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…
This work presents a robust design optimization approach for a char combustion process in a limited-data setting, where simulations of the fluid-solid coupled system are computationally expensive. We integrate a polynomial dimensional…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…