Multilevel Iterative Methods
2020-02-07
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Book Introduction：
Chapter 1:
Linear Vector Spaces and Duals
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This chapter is devoted to some fundamentals of linear vector spaces. First, we define
the linear vector space.
Chapter 2:
Two Grid Method for 1D Elliptic Problem
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Chapter 3:
Basic Linear Iterative Methods
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Chapter 4:
The Preconditioned Conjugate Gradient Method
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Chapter 5:
Auxiliary Spaces and Semi-definite Problems
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Chapter 6:
Singular and Nearly Singular Problems
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Chapter 7:
The Method of Subspace Corrections
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Chapter 8:
Finite Element Subspaces of H(grad), H(curl), H(div) and L2
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Chapter 9:
Locality of High Frequencies and One-level methods
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Chapter 10:
A domain decomposition method
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Chapter 11:
1D Examples
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Chapter 12:
The BPX preconditioner and basic multigrid cycles
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Chapter 13:
Ill-Conditioned Matrices from Well-Posed PDEs: Numerical Artifacts
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Chapter 14:
Sobolev Spaces and Boundary Value Problems
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Chapter 15:
Hilbert Scale for Sobolev spaces
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Chapter 16:
H(grad), H(curl) and H(div) Spaces
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Chapter 17:
Extension of Nodal Variables and Interpolation
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Chapter 18:
Finite Element Discretization for Elliptic PDEs
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Chapter 19:
The Sparse Grid Method
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Chapter 20:
Hierarchical basis methods
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Chapter 21:
Locality of High Frequencies and One-level methods
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Chapter 22:
Introducing Coarse Spaces: From DD to MG (no multigrid theory in this chapter
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Chapter 23:
General Multigrid Methods for H1 systems: theory using elliptic regularity
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Chapter 24:
Multigrid methods for H(div) and H(curl) systems
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Chapter 25:
Multigrid methods for adaptive grids
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Chapter 26:
Auxiliary Grid Methods
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Chapter 27:
Hiptmair-Xu preconditioner for H(curl) and H(div)
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Chapter 28:
Sobolev Spaces and Boundary Value Problems
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