Exponential grids in high-dimensional space
نویسندگان
چکیده
We consider the approximation of functions that are localized in space. We show that it is possible to define meshes to approximate such functions with the property that the number of vertices grows only linearly in dimension. In one dimension, we discuss the optimal mesh for approximating exponentially decreasing functions. We review the use of Cartesian product grids in multiple dimensions introduced in a paper of Bank and Scott [4].
منابع مشابه
Two-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation
In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...
متن کاملTwo-Dimensional Boundary-Conforming Orthogonal Grids for External and Internal Flows Using Schwarz-Christoffel Transformation
In this paper, a Schwarz-Christoffel method for generating two-dimensional grids for a variety of complex internal and external flow configurations based on the numerical integration procedure of the Schwarz-Christoffel transformation has been developed by using Mathematica, which is a general purpose symbolic-numerical-graphical mathematics software. This method is highly accurate (fifth order...
متن کاملStable difference methods for block-structured adaptive grids
The time-dependent Schrödinger equation describes quantum dynamical phenomena. Solving it numerically, the small-scale interactions that are modeled require very fine spatial resolution. At the same time, the solutions are localized and confined to small regions in space. Using the required resolution over the entire high-dimensional domain often makes the model problems intractable due to the ...
متن کاملUnconditionally stable integration of Maxwell's equations
Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicitfinite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general sem...
متن کاملCombination of Adaptive-Grid Embedding and Redistribution Methods on Semi Structured Grids for two-dimensional invisid flows
Among the adaptive-grid methods, redistribution and embedding techniques have been the focus of more attention by researchers. Simultaneous or combined adaptive techniques have also been used. This paper describes a combination of adaptive-grid embedding and redistribution methods on semi-structured grids for two-dimensional invisid flows. Since the grid is semi-structured, it is possible to us...
متن کامل