Explicit volume-preserving splitting methods for polynomial divergence-free vector fields
نویسندگان
چکیده
منابع مشابه
Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields
We present new explicit volume-preserving methods based on splitting for polynomial divergence-free vector fields. The methods can be divided in two classes: methods that distinguish between the diagonal part and the off-diagonal part and methods that do not. For the methods in the first class it is possible to combine different treatments of the diagonal and off-diagonal parts, giving rise to ...
متن کاملExplicit volume-preserving splitting methods for divergence-free ODEs by tensor-product basis decompositions
We discuss the construction of volume-preserving splitting methods based on a tensor product of single-variable basis functions. The vector field is decomposed as the sum of elementary divergence-free vector fields (EDFVFs), each of them corresponding to a basis function. The theory is a generalization of the monomial basis approach introduced in Xue & Zanna (2013, BIT Numer. Math., 53, 265–281...
متن کاملNilpotent normal form for divergence-free vector fields and volume-preserving maps
We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in R has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. ...
متن کاملExplicit geometric integration of polynomial vector fields
We present a unified framework in which to study splitting methods for polynomial vector fields in R. The vector field is to be represented as a sum of shears, each of which can be integrated exactly, and each of which is a function of k < n variables. Each shear must also inherit the structure of the original vector field: we consider Hamiltonian, Poisson, and volumepreserving cases. Each case...
متن کاملTopology-preserving diffusion of divergence-free vector fields and magnetic relaxation
The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, on can find examples of topology-preserving diffusion equations for divergence-free vector fields. They are very degenerate since they admit all stationary solutions to the Euler equations of inc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2012
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-012-0394-0