finite_differences

Finite difference discretization

elementwise_derivative!(coord, f, adv_fac, not_spectral::finite_difference_info)

Calculate the derivative of f using finite differences, with particular scheme specified by coord.finitedifferenceoption; result stored in coord.scratch_2d.

elementwise_derivative!(coord, f, not_spectral::finite_difference_info)

Calculate the derivative of f using 4th order centered finite differences; result stored in coord.scratch_2d.

elementwise_indefinite_integration!(coord, f, not_spectral::finite_difference_info)

Calculate the primitive of f using second-order accurate trapezium rule; result stored in coord.scratch_2d.

take the derivative of input function f and return as df using fourth-order, centered differences. input/output array df is 2D array of size ngrid x nelement

take the derivative of input function f and return as df using second-order, centered differences. input/output array df is 2D array of size ngrid x nelement

take the derivative of input function f and return as df using second-order, centered differences. input/output df is 1D array of size n (full grid)

elementwise_second_derivative!(coord, f, not_spectral::finite_difference_info)

Calculate the second derivative of f using 2nd order centered finite differences; result stored in coord.scratch_2d.

Integrate the input function f and return as pf using second-order trapezium rule. Do the integral on each element separately.

Take the second derivative of input function f and return as df using second-order, centered differences. output array df is 2D array of size ngrid x nelement