Spectral Methods MCQ

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• To make the spectral method advantageous _____________
  ক

  Function must be periodic but grids can be non-uniform

  খ

  Grids should be uniform and function must be periodic

  গ

  Grids should be uniform but function can be non-periodic

  ঘ

  Grids should be structured and function must be periodic
• What is the cost of computation of FFT? (Note: ‘N’ is the number of grid points).
  ক

  N

  খ

  log ⁡N

  গ

  N log ⁡N

  ঘ

  \(\frac{N^2}{2} \)
• The cost of computation for Fourier coefficients can be reduced by ___________
  ক

  FFT

  খ

  DFT

  গ

  IDFT

  ঘ

  IFT
• The cost of computing the Fourier coefficients is ___________ (Note: ‘N’ is the number of grid points).
  ক

  N3

  খ

  N2

  গ

  \(\frac{N^2}{2} \)

  ঘ

  \(\frac{N^3}{3} \)
• Spectral methods are much more accurate than the Finite Difference methods ___________
  ক

  unconditionally

  খ

  conditionally depending on the problem taken

  গ

  conditionally when the number of grid points is small

  ঘ

  conditionally when grid size is small
• For higher order derivatives, spectral methods ___________
  ক

  can be easily generated

  খ

  are not suitable

  গ

  difficult to generate

  ঘ

  become invalid
• What is the advantage of using fourier series in the spectral method?
  ক

  Less grid size

  খ

  Large number of grid points

  গ

  Continuous results

  ঘ

  Flexibility
• What causes aliasing in Spectral methods?
  ক

  Small grid sizes

  খ

  Fourier series

  গ

  Arbitrary values for Fourier series

  ঘ

  Periodic nature
• Spectral methods use ___________
  ক

  Fourier series

  খ

  Taylor series

  গ

  McLaurin series

  ঘ

  Laurent series
• Spectral methods are particularly suitable for __________
  ক

  Subsonic flows

  খ

  Boundary layer flows

  গ

  Compressible flows

  ঘ

  Turbulence modelling