Abstract: Adaptive mesh refinement (AMR) can be used to improve climate simulations since these exhibit features on multiple scales which would be too expensive to resolve using a uniform mesh. In particular, paleo-climate simulations as done in the framework of the German PalMod project only allow for low resolution simulations. Instead of constructing a complex model like an earth system model (ESM) based on AMR, it is desirable to apply the AMR to single components of the existing ESM. We explore the applicability of a forest of trees data structure to incorporate AMR into an existing model. The performance of the data structure is tested by an idealized test case using a numerical scheme for tracer transport in ECHAM6. The numerical results show that the data structure is compatible with the data structure of the original model and also demonstrate improvements of the efficiency compared to non-adaptive meshes.

Abstract: This article proposes a bivariate compensated Volk and Schumaker (CompVSTP) algorithm, which extends the compensated Volk and Schumaker (CompVS) algorithm, to evaluate Bezier tensor product surfaces with floating-point coefficients and coordinates. The CompVSTP algorithm is obtained by applying error-free transformations to improve the traditional Volk and Schumaker tensor product (VSTP) algorithm. We study in detail the forward error analysis of the VSTP, CompVS and CompVSTP algorithms. Our numerical experiments illustrate that the CompVSTP algorithm is much more accurate than the VSTP algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer.