An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;usi...An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.展开更多
为了量化声场中浸入媒介移动对声辐射的影响,基于扩展有限元法(extended finite element method,XFEM)和Dirichlet-Neumann(DtN)构建了一种高效声辐射分析方法,使用该方法分析了媒介边界形状改变对声辐射的影响.XFEM用于建立声场模型,...为了量化声场中浸入媒介移动对声辐射的影响,基于扩展有限元法(extended finite element method,XFEM)和Dirichlet-Neumann(DtN)构建了一种高效声辐射分析方法,使用该方法分析了媒介边界形状改变对声辐射的影响.XFEM用于建立声场模型,其无需修改计算网格仅通过构建拓展函数即可准确捕捉交界面上的非光滑解,引入的水平集函数易于描述边界形状改变.DtN人工边界条件用于准确构建声压及其导数之间的关系,以实现远场辐射条件高效模拟.数值算例表明,所提方法无需重新划分计算网格即可高效表征浸入媒介交界面位置改变,并且多孔材料域的变化会显著改变声辐射特性,实际工程中可在特定位置布置多孔材料获取理想的降噪效果.展开更多
This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite tim...This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.展开更多
文摘An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.
文摘为了量化声场中浸入媒介移动对声辐射的影响,基于扩展有限元法(extended finite element method,XFEM)和Dirichlet-Neumann(DtN)构建了一种高效声辐射分析方法,使用该方法分析了媒介边界形状改变对声辐射的影响.XFEM用于建立声场模型,其无需修改计算网格仅通过构建拓展函数即可准确捕捉交界面上的非光滑解,引入的水平集函数易于描述边界形状改变.DtN人工边界条件用于准确构建声压及其导数之间的关系,以实现远场辐射条件高效模拟.数值算例表明,所提方法无需重新划分计算网格即可高效表征浸入媒介交界面位置改变,并且多孔材料域的变化会显著改变声辐射特性,实际工程中可在特定位置布置多孔材料获取理想的降噪效果.
文摘This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.
