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Table 1 Numerical details for the test cases presented.

From: Certified reduced basis approximation for parametrized partial differential equations and applications

Approximation data

Problem 1

Problem 2

Problem 3

Number of parameters P

2

2

1

Afine op. components Q a

4

9

2

Afine rhs components Q f

1

3

1

FE space dim. N

5,433

16,737

13,976

RB primal space dim. N max pr

21

22

17

RB dual space dim. N max du

30

6

17

RB construction t RB offline (s)

362.8 s

6,733.2 s

2,794.2 s

RB evaluation t RB online (s)

0.107 s

0.198 s

0.158 s

FE evaluation t FE (s)

14.3

41.6

30.2

Computational speedup S

133

210

191

Break-even point Q BE

26

161

93

  1. RB spaces have been built by means of the greedy procedure, using a tolerance ε tol RB = 10 − 2 and a uniform RB greedy train sample of size n train =1,000.
  2. A comparison of the computational times between the Online RB evaluations and the corresponding FE simulations is reported. Here t RB offline is the time of the Offline RB construction and storage, t RB online is the time of an Online RB computation, while t FE is the time for a FE computation, once FE matrices are built. A single timestep is considered in the parabolic cases.