اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHigh Order Accurate Solution of Poissons Equation in Infinite Domains for Smooth Functions
150
0
0.0
(
0
)
تأليف
Christopher R. Anderson
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper a method is presented for evaluating the convolution of the Greens function for the Laplace operator with a specified function $rho(vec x)$ at all grid points in a rectangular domain $Omega subset {mathrm R}^{d}$ ($d = 1,2,3$), i.e. a solution of Poissons equation in an infinite domain. 4th and 6th ord
قيم البحث
اقرأ أيضاً
We solve Poissons equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the le
vels of the multigrid. Numerical experiments solving Poissons equation in the unit square and unit cube show simpl
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $Omega$ with curved boundaries. Given a polygonal approximation $Omega_h$ of the domain $Omega$, the standard order $m$ VEM [6], for $m$ increasing, leads to a
suboptimal convergence rate. We adapt the approach of [16] to VEM and we prove that an optimal convergence rate can be achieved by using a suitable correction depending on high order normal derivatives of the discrete solution at the boundary edges of $Omega_h$, which, to retain computability, is evaluated after applying the projector $Pi^ abla$ onto the space of polynomials. Numerical experiments confirm the theory.
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to con
verge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier-Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization.
This article is an account of the NABUCO project achieved during the summer camp CEMRACS 2019 devoted to geophysical fluids and gravity flows. The goal is to construct finite difference approximations of the transport equation with nonzero incoming b
oundary data that achieve the best possible convergence rate in the maximum norm. We construct, implement and analyze the so-called inverse Lax-Wendroff procedure at the incoming boundary. Optimal convergence rates are obtained by combining sharp stability estimates for extrapolation boundary conditions with numerical boundary layer expansions. We illustrate the results with the Lax-Wendroff and O3 schemes.
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exists a
round the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
