Discrete Solutions of Dirichlet Problems, Finite Volumes, and Circle Packings
نویسندگان
چکیده
منابع مشابه
Cortical cartography using the discrete conformal approach of circle packings.
Cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain. Metric-based approaches are the most common but suffer from high distortions. Conformal, or angle-based algorithms, are supported by a comprehensive mathematical theory. The conformal approach that uses circle packings is versatile in the manipulation and...
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This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f(t, u, v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem a...
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The locations and patterns of functional brain activity in humans are difficult to compare across subjects because of individual differences in cortical folding and the fact that functional foci are often buried within cortical sulci. Cortical flat mapping is a tool which can address these problems by taking advantage of the two-dimensional sheet topology of the cortical surface. Flat mappings ...
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Circle packings are a particularly elegant and simple way to construct quite complicated and elaborate sets in the plane. One systematically constructs a countable family of tangent circles whose radii tend to zero. Although there are many problems in understanding all of the individual values of their radii, there is a particularly simple asymptotic formula for the radii of the circles, origin...
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Given a bounded sequence of integers {d0,d1,d2, . . .}, 6 ≤ dn ≤M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packi...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009447