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We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate solutions and first-order accurate gradients in the L ∞norm on Cartesian grids. The condition number is bounded, regardless of the ratio of the diffusion constant and scales like that of the standard 5-point stencil approximation on a rectangular grid with no interface. Numerical examples are given in two and three spatial dimensions.

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This work presents a general and unified theory describing block copolymer selfassembly in the presence of free surfaces and nanoparticles in the context of Self-Consistent Filed Theory. Specifically, the derived theory applies to free and tethered polymer chains, nanoparticles of any shape, arbitrary non-uniform surface energies and grafting densities, and takes into account a possible formation of triple-junction points (e.g., polymer-air-substrate). One of the main ingredients of the proposed theory is a simple procedure for a consistent imposition of boundary conditions on surfaces with non-zero surface energies and/or non-zero grafting densities that results in singularityfree pressure-like fields, which is crucial for the calculation of forces. The generality of the theory is demonstrated using several representative examples such as the meniscus