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A conservative algorithm for parabolic problems in domains with moving boundaries.

ABSTRACT: We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. Numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward.

SUBMITTER: Novak IL

PROVIDER: S-EPMC4107334 | biostudies-literature | 2014 Aug

REPOSITORIES: biostudies-literature

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A conservative algorithm for parabolic problems in domains with moving boundaries.

Novak Igor L IL Slepchenko Boris M BM

Journal of computational physics 20140801

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due ...[more]

PMID: 25067852

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Project description:BackgroundThe purpose of this study was to extend the analysis of neighborhood effects on child behavioral outcomes in two ways: (1) by examining the geographic extent of the relationship between child behavior and neighborhood physical conditions independent of standard administrative boundaries such as census tracts or block groups and (2) by examining the relationship and geographic extent of geographic peers' behavior and individual child behavior.MethodsThe study neighborhood was a low income, ethnic minority neighborhood of approximately 20,000 residents in a large city in the southwestern United States. Observational data were collected for 11,552 parcels and 1,778 face blocks in the neighborhood over a five week period. Data on child behavior problems were collected from the parents of 261 school-age children (81% African American, 14% Latino) living in the neighborhood. Spatial analysis methods were used to examine the spatial dependence of child behavior problems in relation to physical conditions in the neighborhood for areas surrounding the child's home ranging from a radius of 50 meters to a radius of 1000 meters. Likewise, the spatial dependence of child behavior problems in relation to the behavior problems of neighborhood peers was examined for areas ranging from a radius 255 meters to a radius of 600 meters around the child's home. Finally, we examined the joint influence of neighborhood physical conditions and geographic peers.ResultsPoor conditions of the physical environment of the neighborhood were related to more behavioral problems, and the geographic extent of the physical environment that mattered was an area with a radius between 400 and 800 meters surrounding the child's home. In addition, the average level of behavior problems of neighborhood peers within 255 meters of the child's home was also positively associated with child behavior problems. Furthermore, these effects were independent of one another.ConclusionsThese findings demonstrate that using flexible geographies in the study of neighborhood effects can provide important insights into spatial influences on health outcomes. With regards to child behavioral outcomes, specifically, these findings support the importance of addressing the physical and social environment when planning community-level interventions to reduce child behavior problems.

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A conservative algorithm for parabolic problems in domains with moving boundaries.

Publications

A conservative algorithm for parabolic problems in domains with moving boundaries.

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