List of Tables

Chapter 3: Data Structures

Table 15.1: Pros and cons of linear and high-order finite elements. It is assumed that the same number of degrees of freedom (unknowns) is used in both methods.

Table 18.1: Number of symmetric Gauss Seidel (or Jacobi) relaxations used within PCG applied to four SPD stiffness matrices (examples 2 to 5 in the file "bcsstruc2.data" in the Harwell Boeing collection), where order is the matrix order and nonzeroes is the number of nonzero elements in the entire matrix.

Table 19.1: Number of PCG iterations used in each refinement level in the adaptive-refinement algorithm (with threshold of 0.01 and automatic boundary refinement) applied to the diffusion example. The computation time of a multigrid iteration is the same as that of five symmetric Gauss Seidel iterations. (The setup time is negligible.)
Table 19.2: Number of PCG iterations used in each refinement level in the adaptive-refinement algorithm (with threshold of 0.01 and automatic boundary refinement) applied to an implicit time-marching step (with ?t = 1) in the time-dependent diffusion example.

Table 20.1: The adaptive-refinement algorithm (with automatic boundary refinement) applied to the linear elasticity equations in the circle (with Poisson ratio ? = 1/3). The modified multigrid preconditioner costs the same as five symmetric Gauss Seidel iterations. (The setup time is negligible.)

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