TY - JOUR
T1 - On the efficiency and accuracy of interpolation methods for spectral codes
AU - Hinsberg, van, M.A.T.
AU - Thije Boonkkamp, ten, J.H.M.
AU - Toschi, F.
AU - Clercx, H.J.H.
PY - 2012
Y1 - 2012
N2 - In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be explained. Furthermore, a fast implementation of the interpolation methods is given. We show that the B-spline-based interpolation method has several advantages compared to other methods. First, the order of continuity of the interpolated field is higher than for other methods. Second, only one FFT is needed, whereas, for example, Hermite interpolation needs multiple FFTs for computing the derivatives. Third, the interpolation error almost matches that of Hermite interpolation, a property not reached by other methods investigated.
AB - In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way many properties like order of continuity, order of convergence, and magnitude of errors can be explained. Furthermore, a fast implementation of the interpolation methods is given. We show that the B-spline-based interpolation method has several advantages compared to other methods. First, the order of continuity of the interpolated field is higher than for other methods. Second, only one FFT is needed, whereas, for example, Hermite interpolation needs multiple FFTs for computing the derivatives. Third, the interpolation error almost matches that of Hermite interpolation, a property not reached by other methods investigated.
U2 - 10.1137/110849018
DO - 10.1137/110849018
M3 - Article
VL - 34
SP - B479-B498
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
SN - 1064-8275
IS - 4
ER -