| Contents |
Spectral/pseudospectral methods have been successfully applied to seek approximation solutions to smooth problems for decades. However, it is also known that these methods may suffer from serious rounding errors due to the ill-conditioned numerical differentiation, if great care is not exercised. To resolve this issue many integration preconditioning approaches have been developed, mostly on a single domain formulation. In this talk we will present an integration preconditioning approach with low-rank updates to construct inverse and preconditioning matrices for multidomain pseudospectral advection and diffusion operators. By applying these matrices, the resultant preconditioned schemes can be efficiently solved with computation steps only proportional to the number of subdomains and independent of the degree of the approximation polynomials. Such an efficiency of the method is supported by theoretical arguments and have been observed in numerical experiments. Issues related to further developments of the proposed integration preconditioning approach will be discussed. |