4 citations · 5 across the 14 of their papers we have counts for
15 papers
Tensor-Based Reduced-Order Modeling for Optimization-Based Inverse Problems
Sahidul Islam, Andreas Mang, Maxim Olshanskii
We develop a tensor reduced-order modeling (TROM) framework for optimization-based inverse problems governed by parameter-dependent dynamical systems. The approach approximates the…
Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows
Md Rezwan Bin Mizan, Ilya Timofeyev, Maxim Olshanskii
We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. T…
Tensorial Reduced-Order Models for Parametric Coupled Reaction-Diffusion Systems: Application to Brain Tumor Growth Modeling
Asikul Islam, Md Rezwan Bin Mizan, Maxim Olshanskii +1
We construct efficient surrogate models for parametric forward operators arising in brain tumor growth simulations, governed by coupled semilinear parabolic reaction-diffusion syst…
A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations
Zhanybek Baitulenov, Maxim Olshanskii, Almas Temirbekov +2
This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the moti…
An unfitted divergence-free higher order finite element method for the Stokes problem
Michael Neilan, Maxim Olshanskii, Henry von Wahl
The paper develops and analyzes a higher-order unfitted finite element method for the incompressible Stokes equations, which yields a strongly divergence-free velocity field up to…
Low-rank cross approximation of function-valued tensors for reduced-order modeling of parametric PDEs
Stanislav Budzinskiy, Vladimir Kazeev, Maxim Olshanskii
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field,…
A Stabilized Trace FEM for Surface Cahn--Hilliard Equations: Analysis and Simulations
Deepika Garg, Maxim Olshanskii
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines th…
An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time
Santolo Leveque, Yunhui He, Maxim Olshanskii
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to b…
A parametric tensor ROM for the shallow water dam break problem
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model red…
Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-D…
Projected gradient stabilization of sharp and diffuse interface formulations in unfitted Nitsche finite element methods
Maxim Olshanskii, Jan-Phillip Bäcker, Dmitri Kuzmin
We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operato…
Stability of instantaneous pressures in an Eulerian finite element method for moving boundary flow problems
Maxim Olshanskii, Henry von Wahl
This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method fo…
A preconditioner for the grad-div stabilized equal-order finite elements discretizations of the Oseen problem
Yunhui He, Maxim Olshanskii
The paper considers grad-div stabilized equal-order finite elements (FE) methods for the linearized Navier-Stokes equations. A block triangular preconditioner for the resulting sys…
A narrow band finite element method for the level set equation
Maxim Olshanskii, Arnold Reusken, Paul Schwering
A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band aroun…
A conservative Eulerian finite element method for transport and diffusion in moving domains
Maxim Olshanskii, Henry von Wahl
The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-depe…