This dissertation presents an efficient and high-order boundary integral solver for the Stokes equations in complex 3D geometries. The targeted applications of this solver are the flow problems in domains involving moving boundaries. In such problems, traditional finite element methods involving 3D unstructured mesh generation experience difficulties. Our solver uses the indirect boundary integ...

In this paper, we develop a boundary integral method (BIM) for interacting particles in unsteady Stokes flow or linear viscoelastic (LVE) flow. The idea is to exploit a correspondence principle between them so a BIM can be established in the Fourier domain. Since the unsteady Stokes equation in the frequency domain is analogous to Brinkman equation in the time domain, our method can also be use...

We describe how the Borel summability of a divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for non-analytic initial data, the present approach generates an integral equation (IE) applicable to much more general data. We apply these concepts to the three-dimensional Navier-Stokes (NS) system and s...

An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the algorithm scales as O(N) or O(N logN), where N is proportional to the product of number of particles and the number of elements employed to discretize the particl...

We want to study the perturbation growth of an initial seed of an ellipsoidal shape in Top-Hat collapse model of the structure formation in the Modied Chaplygin gas cosmology. Considering reasonable values of the constants and the parameters of the model under study, we can show that a very small deviation from spherical symmetry (ellipsoidal geometry) in the initial seed leads to a nal highly ...

We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N)/[(U(1)]N−1 space. We then introduce the relativistic quark-monopole interaction as a Wess–Zumino-type action, and extend it to the non-abelian case. We show that condensation of monopoles and confinement can be inves...

A three-dimensional inverse problem dealing with the reconstruction of cavities in a uniform semi-infinite solid from surface elastodynamic waveforms is investigated via the linear sampling method. To cater for active imaging applications that are often characterized by a limited density of illuminating sources, the existing near-field formulation of the linear sampling method is advanced in te...

We study a distance between shapes defined by minimizing the integral of kinetic energy along transport paths constrained to measures with characteristic-function densities. The formal geodesic equations for this shape distance are Euler equations for incompressible, inviscid potential flow of fluid with zero pressure and surface tension on the free boundary. The minimization problem exhibits a...

Recently, the free boundary problem of quasistationary Stokes flow of a mass of viscous liquid under the action of surface tension forces has been considered by R.W. HOPPER, L.K. ANTANOVSKII, and others. The solution of the Stokes equations is represented by analytic functions, and a time dependent. conformal mapping ont.o the flow domain is applied for the t.ransformation of the problem to the...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...