3.4 Evaluation of the Discrete Forms

In this section a list of operations for computing the discrete operators is given. The programme of computation is given prominence because it needs to be executed for each quadrature point and hence it is the key to determining the computational cost of the overall method. The following computational programme is intended to be optimal. Note that it is assumed that p and v_p are already set.

A: Set q the point on the element

B: Set n_q the unit outward normal to the element at q

C: Compute v_p.n_q

D: Compute r

E: Compute r, r²

F: Compute r³ (in the 3D case)

G: Compute [śr/ śn_q] via (22)

H: Compute [śr/ śv_p] via (23)

I: Compute

[śr/śn_q] *[śr/ śv_p]

J: Compute [ś² r/ śv_p śn_q] via (24)

Apart from operations E and M, each operation can be directly costed in terms of floating-point operations. Operation E computes a square root. In the subroutines L2LC, L3LC and L3ALC the square root function need to be provided as an external functions with the identifier FNSQRT. Within this the standard Fortran square root function or a user-defined alternative may be employed.

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