Related papers: Numerical Solution of the Steady-State Navier-Stok…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We investigate the temporal accuracy of two generalized-$\alpha$ schemes for the incompressible Navier-Stokes equations. The conventional approach treats the pressure with the backward Euler method while discretizing the remainder of the…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…
In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…
The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and…
Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is…
In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…
We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…