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We propose efficient pseudospectral numerical schemes for solving the self-consistent, mean-field equations for inhomogeneous polymers. In particular, we introduce a robust class of semi-implicit methods that employ asymptotic small scale information about the nonlocal density operators. The relaxation schemes are further embedded in a multilevel strategy… (More)

Boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities. In addition, surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics. This makes the spatial discretization even more difficult and, at the same time, imposes a severe time step constraint for stable… (More)

We introduce a method for solving the variable coefficient Poisson equation on non-graded Cartesian grids that yields second order accuracy for the solutions and their gradients. We employ quadtree (in 2D) and octree (in 3D) data structures as an efficient means to represent the Cartesian grid, allowing for constraint-free grid generation. The schemes take… (More)

The Immersed Boundary Method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit dis-cretizations. This excessive stability constraint can… (More)

We present a nonstiff, fully adaptive mesh refinement-based method for the Cahn-Hilliard equation. The method is based on a semi-implicit splitting, in which linear leading order terms are extracted and discretized implicitly, combined with a robust adaptive spatial discretization. The fully discretized equation is written as a system which is efficiently… (More)

We present an efficient numerical methodology for the 3D computation of incom-pressible multi-phase flows described by conservative phase field models. We focus here on the case of density matched fluids with different viscosity (Model H). The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time… (More)

We propose a fast and non-stiff approach for the solutions of the Immersed Boundary Method, for Newtonian, incompressible flows in two or three dimensions. The proposed methodology is built on a robust semi-implicit dis-cretization introduced by Peskin in the late 70's which is solved efficiently through the novel use of a fast, treecode strategy to compute… (More)

We present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations (SDEs). The method is an adaptation of the semi-implicit backward differential formula (SBDF) multistep method for deterministic differential equations and allows for a semi-implicit discretization of the drift term to… (More)

We propose a novel approach for the numerical integration of diffusion-type equations with variable and degenerate mobility or diffusion coefficient. Our focus is the Cahn-Hilliard equation which plays a prominent role in phase field models of fluids and soft materials but the methodology has a more general applicability. The central idea is a split method… (More)

Boundary integral methods have been used widely for the simulation of interfacial Stokes flows. These free surface representations reduce the problem to one defined solely on the fluid interface. Often the assumption of axi-symmetry is used to further reduce the dimensionality of the problem. However, it is difficult to obtain high order approximations to… (More)