A Fast Grid Adaption Scheme for Elliptic Partial Differential Equations

نویسنده

  • Calvin J. Ribbens
چکیده

We describe the R.eeursilJe Subdivision (RS) grid adaption method-an efficient and effective adaptive grid scheme for two-dimensional, elliptic partial differential equations (PDEs). The RS method generates a new grid by recursively subdividing a rectangular domain. We use a heuristic approach which attempts to equidistribute a given density function over the domain. The resulting grid is used to generate an adapHve grid domain mapping, which may be applied to transform the PDE problem to another coordinate system. The PDE is then solved in the transformed coordinate system using a uniform grid. The RS method generates good adaptive grids at a small cost compared to the cost of the entire computation. We describe the algorithm in detail and demonstrate the effectiveness of our scheme on two realistic test problems.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Fast Direct Solver for a Class of Elliptic Partial Differential Equations

We describe a fast and robust method for solving the large sparse linear systems that arise upon the discretization of elliptic partial differential equations such as Laplace’s equation and the Helmholtz equation at low frequencies. While most existing fast schemes for this task rely on so called “iterative” solvers, the method described here solves the linear system directly (to within an arbi...

متن کامل

A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method

In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.

متن کامل

The Stability of Non-standard Finite Difference Scheme for Solution of Partial Differential Equations of Fractional Order

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order are called fractional partial differential equations (FPDEs). Recently, these equations have received special attention due to their high practical applications. In this paper, we survey a rather general case of FPDE t...

متن کامل

The new implicit finite difference scheme for two-sided space-time fractional partial differential equation

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

متن کامل

für Mathematik in den Naturwissenschaften Leipzig Multi - Grid Methods for FEM and BEM Applications by Wolfgang

After discretisation of the partial differential equations from mechanics one usually obtains large systems of (non)linear equations. Their efficient solution requires the use of fast iterative methods. Multi-grid iterations are able to solve linear and nonlinear systems with a rather fast rate of convergence, provided the problem is of elliptic type. The contribution describes the basic constr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013