Irregular problems require the computation of some properties of a set of elements irregularly distributed in a domain. These problems satisfy a locality property because the properties of an element e depend upon those of its neighbors according to a problem dependent stencil. This paper proposes two strategies, fault prevention and informed fault prevention, to collect properties of elements ...

In this paper, a hybrid of Local Domain Free Discretization and Immersed Boundary Method (termed as LDFD-IBM), is applied to simulate the incompressible flow over four circular cylinders in an in-line square configuration. LDFD-IBM belongs to the family of "Cartesian mesh methods", which means the complication of mesh generation is avoided for the problems with complex geometries. A Stencil Ada...

We propose an algorithm for interpolation of two-dimensional curves using Euler spirals. The method uses a lower order reconstruction to approximate solution derivatives at each sample point. The computed tangents are then used to connect consecutive points with segments of Euler spirals. The resulting interpolation is G in regions where the curve being interpolated is smooth. The algorithm use...

We design adaptive finite differences discretizations, which are degenerate elliptic and second order consistent, of linear quasi-linear partial differential operators featuring both a first term ananisotropicsecond term. Our approach requires the domain to be discretized on Cartesian grid, takes advantage techniques from field low-dimensional lattice geometry. prove that stenc...

In a previous paper by Ryan and Shu [Ryan, J. K., and Shu, C.-W. (2003). Methods Appl. Anal. 10(2), 295–307], a one-sided post-processing technique for the discontinuous Galerkin method was introduced for reconstructing solutions near computational boundaries and discontinuities in the boundaries, as well as for changes in mesh size. This technique requires prior knowledge of the discontinuity ...

Controlled synthesis and integration of carbon nanotubes (CNTs) remain important areas of study to develop practical carbon-based nanodevices. A method of controlling the number of CNTs synthesized depending on the size of the catalyst was characterized using nanostencil lithography, and the critical dimension for the nanoaperture produced on a stencil mask used for growing individual CNTs was ...

Adaptive multigrid methods solve partial differential equations through a discrete representation of the domain that introduces more points in those zones where the equation behavior is highly irregular. The distribution of the points changes at run time in a way that cannot be foreseen in advance. We propose a methodology to develop a highly parallel solution based upon a load balancing strate...

Precise spatial positioning and isolation of mammalian cells is a critical component of many single cell experimental methods and biological engineering applications. Although a variety of cell patterning methods have been demonstrated, many of these methods subject cells to high stress environments, discriminate against certain phenotypes, or are a challenge to implement. Here, we demonstrate ...

The use of adaptive mesh spatial discretisation methods, coupled spatial and temporal error control and domain decomposition methods make it possible to construct efficient automatic methods for the numerical solution of time-dependent Navier Stokes problems. This paper describes the unstructured triangular mesh spatial discretisation method being used in a prototype package for compressible fl...

This paper describes a new technique for optimizing serial and parallel stencil-and stencil-like operations for cache-based architectures. This technique takes advantage of the semantic knowledge implicitly in stencil-like computations. The technique is implemented as a source-to-source program transformation; because of its speci-city it could not be expected of a conventional compiler. Empiri...