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Order‐Optimal Preconditioners for Implicit Runge–Kutta Schemes Applied to Parabolic PDEs

✍ Scribed by Mardal, K.‐A.; Nilssen, T. K.; Staff, G. A.


Book ID
118190936
Publisher
Society for Industrial and Applied Mathematics
Year
2007
Tongue
English
Weight
189 KB
Volume
29
Category
Article
ISSN
1064-8275

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Order optimal preconditioners for fully
✍ Trygve K. Nilssen; Gunnar A. Staff; Kent-Andre Mardal 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 869 KB

The partial differential equation part of the bidomain equations is discretized in time with fully implicit Runge-Kutta methods, and the resulting block systems are preconditioned with a block diagonal preconditioner. By studying the time-stepping operator in the proper Sobolev spaces, we show that