Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries...Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries are close to each other.We present a boundary integralmethod in two dimensions which is specially designed tomaintain second order accuracy even if boundaries are arbitrarily close.Themethod uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy.For boundaries with many components we use the fast multipolemethod for efficient summation.We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium.We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals.Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region.A number of examples are presented.We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.展开更多
A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the ...A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the free-spaceGreen’s function.To evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate charts.High order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic analysis.Numerical tests demonstrate the uniform convergence rates of the method.展开更多
文摘Boundary integral methods are naturally suited for the computation of harmonic functions on a region having inclusions or cells with different material properties.However,accuracy deteriorates when the cell boundaries are close to each other.We present a boundary integralmethod in two dimensions which is specially designed tomaintain second order accuracy even if boundaries are arbitrarily close.Themethod uses a regularization of the integral kernel which admits analytically determined corrections to maintain accuracy.For boundaries with many components we use the fast multipolemethod for efficient summation.We compute electric potentials on a domain with cells whose conductivity differs from that of the surrounding medium.We first solve an integral equation for a source term on the cell interfaces and then find values of the potential near the interfaces via integrals.Finally we use a Poisson solver to extend the potential to a regular grid covering the entire region.A number of examples are presented.We demonstrate that increased refinement is not needed to maintain accuracy as interfaces become very close.
文摘A straightforward method is presented for computing three-dimensional Stokes flow,due to forces on a surface,with high accuracy at points near the surface.The flowquantities arewritten as boundary integrals using the free-spaceGreen’s function.To evaluate the integrals near the boundary,the singular kernels are regularized and a simple quadrature is applied in coordinate charts.High order accuracy is obtained by adding special corrections for the regularization and discretization errors,derived here using local asymptotic analysis.Numerical tests demonstrate the uniform convergence rates of the method.
