We consider a coupled problem of Stokes and Darcy equations. This involves solving PDEs different orders simultaneously. To overcome this difficulty, we apply nonoverlapping domain decomposition method based on Robin boundary condition obtained by combining the velocity force interface conditions. The system is then reduced to each separately an iterative procedure using Krylov subspace method. numerical solution in subdomain integral formulation, where kernels are regularized correction...

A kernel-independent treecode (KITC) is presented for fast summation of particle interactions. The method employs barycentric Lagrange interpolation at Chebyshev points to approximate well-separated particle-cluster KITC requires only kernel evaluations, suitable non-oscillatory kernels, and it utilizes a scale-invariance property interpolation. For given level accuracy, the reduces operation count pairwise interactions from $O(N^2)$ $O(N\log N)$, where $N$ number particles in system....

Abstract 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 flow quantities are written as boundary integrals using free-space Green’s function. To evaluate boundary, singular kernels regularized and simple quadrature applied in coordinate charts. High order obtained by adding special corrections regularization discretization errors, derived here local asymptotic analysis. Numerical...

The Stokeslet and stresslet kernels are commonly used in boundary element simulations singularity methods for slow viscous flow. Evaluating the velocity induced by a collection of Stokeslets stresslets direct summation requires $O(N^2)$ operations, where $N$ is system size. present work develops treecode algorithm 3D that reduces cost to $O(N\log N)$. particles divided into hierarchy clusters, well-separated particle-cluster interactions computed far-field Cartesian Taylor approximation....

Treecode algorithms efficiently approximate N-body interactions in O(N) or O(NlogN). In order to treat general 3D kernels, recent developments employ polynomial interpolation the kernels. The polynomials are a tensor product of 1-dimensional polynomials. Here, we develop an O(NlogN) tricubic based treecode method for is inherently three-dimensional and as such does not product. form allows easy evaluation derivatives kernel, required dynamical simulations, which case approach. We both...

Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous where the Reynolds number is small. Boundary integral equations often used to solve these problems, fundamental solutions for velocity Stokeslet and stresslet. One of main challenges evaluating boundary integrals that kernels become singular on surface. A regularization method eliminates singularities reduces numerical error through correction terms both stresslet was developed Tlupova Beale, JCP (2019)....

We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, harmonic potentials Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral equation one is close to another obtain grid points. replace the kernel with regularized version having length parameter $\delta$ order control discretization error. Analysis near singularity leads expression error due regularization which has terms unknown...

We present a simple yet accurate method to compute the adjoint double layer potential, which is used solve Neumann boundary value problem for Laplace's equation in three dimensions. An expansion curvilinear coordinates leads us modify expression so that singularity reduced when evaluating integral on surface. then regularize Green's function, with radial parameter $\delta$. show natural regularization has error $O(\delta^3)$, and modification improves $O(\delta^5)$. The evaluated numerically...

Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous where the Reynolds number is small. Boundary integral equations often used to solve these problems, fundamental solutions for velocity Stokeslet and stresslet. One of main challenges evaluating boundary integrals that kernels become singular on surface. A regularization method eliminates singularities reduces numerical error through correction terms both stresslet was developed Tlupova Beale, JCP (2019)....