Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

Estimates of electronic coupling for excess electron transfer in DNA

Electronic coupling Vda is one of the key parameters that determine the rate of charge transfer through DNA. While there have been several computational studies of Vda for hole transfer, estimates of electronic couplings for excess electron transfer (ET) in DNA remain unavailable. In the paper, an efficient strategy is established for calculating the ET matrix elements between base pairs in a π stack. Two approaches are considered. First, we employ the diabatic-state (DS) method in which donor and acceptor are represented with radical anions of the canonical base pairs adenine-thymine (AT) and guanine-cytosine (GC). In this approach, similar values of Vda are obtained with the standard 6-31 G* and extended 6-31++ G* basis sets. Second, the electronic couplings are derived from lowest unoccupied molecular orbitals (LUMOs) of neutral systems by using the generalized Mulliken-Hush or fragment charge methods. Because the radical-anion states of AT and GC are well reproduced by LUMOs of the neutral base pairs calculated without diffuse functions, the estimated values of Vda are in good agreement with the couplings obtained for radical-anion states using the DS method. However, when the calculation of a neutral stack is carried out with diffuse functions, LUMOs of the system exhibit the dipole-bound character and cannot be used for estimating electronic couplings. Our calculations suggest that the ET matrix elements Vda for models containing intrastrand thymine and cytosine bases are essentially larger than the couplings in complexes with interstrand pyrimidine bases. The matrix elements for excess electron transfer are found to be considerably smaller than the corresponding values for hole transfer and to be very responsive to structural changes in a DNA stack

A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.