Related papers: A Numerical Approach to Solving Nonlinear Differen…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations.…
A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…
In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous…
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel…
This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently…
There has been significant progress in the development of quantum algorithms for solving linear systems of equations with a growing body of applications to Computational Fluid Dynamics (CFD) and CFD-like problems. This work extends previous…
In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
Data-driven methods for computer simulations are blooming in many scientific areas. The traditional approach to simulating physical behaviors relies on solving partial differential equations (PDE). Since calculating these iterative…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…
Numerical solutions of 2-D steady incompressible flow inside a triangular cavity are presented. For the purpose of comparing our results with several different triangular cavity studies with different triangle geometries, a general triangle…
This paper introduces an inviscid Computational Fluid Dynamics (CFD) approach for the rapid aerodynamic assessment of Flettner rotor systems on ships. The method relies on the Eulerian flow equations, approximated utilizing a…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…