Computer Simulation of Stochastic Wind Velocity Fields for Structural Response Analysis: Comparisons and Applications

Table 1

Two-steps implementation of the considered simulation methods and corresponding memory allocation for a 2N-variate process (the symbol ∝ denotes proportionality).

	WAWS	POD	AR
Phase 0	calculate 2𝑁⋅𝑁𝜔 Cholesky matrices 𝐓(𝜔𝑟𝑘) of dimension 2𝑁×2𝑁 and store 2𝑁⋅𝑁𝜔 column vectors 𝑇∶,𝑟(𝜔𝑟𝑘) of length 2𝑁	calculate and store 𝑁𝜔 matrices of eigenvectors 𝜽𝑟^(𝑘) of dimension 2𝑁×2𝑁 and 2𝑁⋅𝑁𝜔 eigenvalues 𝛾𝑟^(𝑘)	calculate and store 𝑝1 matrices Φ𝑖 of dimension 2𝑁×2𝑁 and one matrix 𝐁0 of dimension 2𝑁×2𝑁
Phase 1	sum 𝑁(2𝑁+1)𝑁𝜔 scalar numbers and perform 𝑁(2𝑁+1) inverse FFTs	perform 𝑁𝜔 interpolations of 𝛾𝑟^(𝑘) and 𝜽𝑟^(𝑘), sum 𝑁𝜔⋅(2𝑁+1) vectors of length 2𝑁 and perform 2𝑁 inverse FFTs	perform (𝑝1+1)𝑁𝑡 multiplications of matrices Φ𝑖 and 𝐁0by vectors of length 2𝑁 and sum (𝑝1+1)𝑁𝑡 vectors of length 2𝑁
Allocated memory in phase 0	∝(2𝑁)^2𝑁𝜔	∝(2𝑁)^2𝑁𝜔	∝(2𝑁)^2(𝑝1+1)