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Topics in Structure-preserving Discretization by Snorre H. Christiansen; Hans Z. Munthe-Kaas; Brynjulf Owren is a nonfiction available to read on EtoBox.
What is Topics in Structure-preserving Discretization about?
In the last few decades the concepts of structure-preserving discretization, geometric integration and compatible discretizations have emerged as subfields in the numerical approximation of ordinary and partial differential equations. The article discusses certain selected topics within these areas; discretization techniques both in space and time are considered. Lie group integrators are discussed with particular focus on the application to partial differential equations, followed by a discussion of how time integrators can be designed to preserve first integrals in the differential equation using discrete gradients and discrete variational derivatives. Lie group integrators depend crucially on fast and structure-preserving algorithms for computing matrix exponentials. Preservation of domain symmetries is of particular interest in the application of Lie group integrators to PDEs. The equivariance of linear operators and Fourier transforms on non-commutative groups is used to construct fast structure-preserving algorithms for computing exponentials. The theory of Weyl groups is employed in the construction of high-order spectral element discretizations, based on multivariate Chebys
Who reads Topics in Structure-preserving Discretization?
It is typically read by self-directed learners exploring a subject in depth.
Common subject areas: history, science, philosophy, social sciences.
- Author
- Snorre H. Christiansen; Hans Z. Munthe-Kaas; Brynjulf Owren
- Publisher
- Cambridge University Press (CUP)
- Published
- 2011
- Language
- EN
- ISBN
- 9781107010864
- Category
- nonfiction
- Subjects
- Mathematics, Stem
