In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clif...In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.展开更多
In this article,we present two new novel finite difference approximations of order two and four,respectively,for the three dimensional non-linear triharmonic partial differential equations on a compact stencil where t...In this article,we present two new novel finite difference approximations of order two and four,respectively,for the three dimensional non-linear triharmonic partial differential equations on a compact stencil where the values of u,δ^(2)u/δn^(2)andδ^(4)u/δn^(4)are prescribed on the boundary.We introduce new ideas to handle the boundary conditions and there is no need to discretize the derivative boundary conditions.We require only 7-and 19-grid points on the compact cell for the second and fourth order approximation,respectively.The Laplacian and the biharmonic of the solution are obtained as by-product of the methods.We require only system of three equations to obtain the solution.Numerical results are provided to illustrate the usefulness of the proposed methods.展开更多
In this paper,we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation.By s...In this paper,we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation.By solving simple linear equations,the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points.This is a generalization of previous works on Plateau-Bezier problem,harmonic,biharmonic and quasi-harmonic Bézier surfaces.Some representative examples show the effectiveness of the presented method.展开更多
In this paper,the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.The Dirichlet problem for this triharmonic equation is reca...In this paper,the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however,do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain.This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy.The analysis is further generalized to polyharmonic equations.展开更多
基金supported by NNSF for Young Scholars of China(11001206)
文摘In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.
基金This research was supported by’The University of Delhi’under research grant No.Dean(R)/R&D/2010/1311.
文摘In this article,we present two new novel finite difference approximations of order two and four,respectively,for the three dimensional non-linear triharmonic partial differential equations on a compact stencil where the values of u,δ^(2)u/δn^(2)andδ^(4)u/δn^(4)are prescribed on the boundary.We introduce new ideas to handle the boundary conditions and there is no need to discretize the derivative boundary conditions.We require only 7-and 19-grid points on the compact cell for the second and fourth order approximation,respectively.The Laplacian and the biharmonic of the solution are obtained as by-product of the methods.We require only system of three equations to obtain the solution.Numerical results are provided to illustrate the usefulness of the proposed methods.
基金supported by the National Natural Science Foundation of China(No.11801225)University Science Research Project of Jiangsu Province(No.18KJB110005)the Research Foundation for Advanced Talents of Jiangsu University(No.14JDG034).
文摘In this paper,we present a method for generating Bézier surfaces from the boundary information based on a general second order functional and a third order functional associated with the triharmonic equation.By solving simple linear equations,the internal control points of the resulting Bézier surface can be obtained as linear combinations of the given boundary control points.This is a generalization of previous works on Plateau-Bezier problem,harmonic,biharmonic and quasi-harmonic Bézier surfaces.Some representative examples show the effectiveness of the presented method.
文摘In this paper,the two-dimensional slowly rotating highly viscous fluid flow in small cavities is modelled by the triharmonic equation for the streamfunction.The Dirichlet problem for this triharmonic equation is recast as a set of three boundary integral equations which however,do not have a unique solution for three exceptional geometries of the boundary curve surrounding the planar solution domain.This defect can be removed either by using modified fundamental solutions or by adding two supplementary boundary integral conditions which the solution of the boundary integral equations must satisfy.The analysis is further generalized to polyharmonic equations.
