Related papers: Fast Solution of the Linearized Poisson-Boltzmann …
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution and a set of indices…
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…
In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…
An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…
We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate the frequency-domain PDE, we take advantage of…
In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be…
In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navier-Stokes and Cahn-Hilliard problems. The full order finite…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
The use of model-based numerical simulation of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively and this is computationally expensive. We present a…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
To accurately model the electron density and polarization, a polarizable multipole (PM) model using the AMOEBA force field has been introduced \cite{Ren:2003, Shi:2013} recently. In the AMOEBA force field, the traditional point atomic…
Biomolecular electrostatics is key in protein function and the chemical processes affecting it. Implicit-solvent models via the Poisson-Boltzmann (PB) equation provide insights with less computational cost than atomistic models, making…
For numerical approximation the reformulation of a PDE as a residual minimisation problem has the advantages that the resulting linear system is symmetric positive definite, and that the norm of the residual provides an a posteriori error…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
This paper considers the analysis of partial differential equations (PDE) containing multiple random variables. Recently developed collocation methods enable the construction of high-order stochastic solutions by converting a stochastic PDE…
The Poisson-Boltzmann (PB) model is a widely used implicit solvent model in protein simulations. Although variants, such as the size modified PB and nonlocal modified PB models, have been developed to account for ionic size effects and…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
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…