Wave Equation Simulation on Manifold using Discrete Exterior Calculus
نویسندگان
چکیده
Numerical simulation provides a effective tool for studying both the spatial and temporal nature of acoustic field on 3D or 4D timespace. The paper deals with the description of discrete exterior calculus scheme for the wave equation. This method can be directly implemented on manifold, which is the generation of finite difference time domain method from flat space to curved space.
منابع مشابه
Computational Electromagnetism and Implicit Discrete Exterior Calculus
The implicit Euler scheme of time variable and discrete exterior calculus can be united to find an unconditional stable approach, which is called implicit discrete exterior calculus. This technique for solving Maxwell’s equations in time domain is discussed, which provides flexibility in numerical computing on manifold. For some problems, it takes much less computational time to use the implici...
متن کاملDiscrete Wheeler-DeWitt Equation
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3geometries is replaced by a space of three-dimensional piecewise linear spaces, with the solutions to the lattice equations providing a suitable approximation to the continuum wave functional. The equations incorpor...
متن کاملar X iv : m at h - ph / 0 60 10 15 v 1 9 J an 2 00 6 DIFFERENTIAL COMPLEXES AND EXTERIOR CALCULUS
In this paper we present a new theory of exterior calculus over k-dimensional domains in a smooth n-manifold, unifying the discrete and continuum theories. The discrete theory carries a full set of classical operators, products, and relations of calculus and geometry and is free from the standard problems encountered in other theories of discrete exterior calculus. It is based on the Koszul com...
متن کاملNumerical method for Darcy flow derived using Discrete Exterior Calculus
We derive a numerical method for Darcy flow, hence also for Poisson’s equation in first order form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is its discretization on simplicial complexes such as triangle and tetrahedral meshes. We start by rewriting the governing equations of Darcy flow using the language of ...
متن کاملComputations for Analysis, Geometry and Topology
My research agenda is built on formulating problems in analysis, geometry and topology for a computational realization and conversely, use of computation for formalizing notions in analysis, geometry and topology. The former stems from a motivation to provide solutions for problems in science and engineering using tools of scientific and high performance computing while the latter encapsulates ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009