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Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…
This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…
We propose to analyse the discretization of the Stokes problem with nonconforming finite elements in light of the T-coercivity (cf. [1] for Helmholtz-like problems, see [2], [3] and [4] for the neutron diffusion equation). We propose…
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…
A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the method is to transform the governing equations to a boundary…
We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS)…
Numerical simulation of incompressible fluid flows has been an active topic of research in Scientific Computing for many years, with many contributions to both discretizations and linear and nonlinear solvers. In this work, we propose an…
The Stokes equation posed on surfaces is important in some physical models, but its numerical solution poses several challenges not encountered in the corresponding Euclidean setting. These include the fact that the velocity vector should…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…
We propose a $p$-multilevel preconditioner for Hybrid High-Order discretizations (HHO) of the Stokes equation, numerically assess its performance on two variants of the method, and compare with a classical Discontinuous Galerkin scheme. We…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…
We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…
In this work, we compare the nodal and isogeometric spatial discretization schemes for the nonlinear formulation of shear- and torsion-free rods introduced in [1]. We investigate the resulting discrete solution space, the accuracy, and the…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…