Minisymposium

Dynamic adaptive mesh refinement has proven to be a successful tool in reducing the error of scientific simulations, while maintaining competitive runtimes. By refining the mesh locally in areas of interest, the computational power and memory consumption is reduced by orders of magnitude compared to uniform meshes. However, the parallel management of adaptive meshes and their associated data is a challenging task and should be outsourced to third-party libraries. We present the open-source library t8code for scalable AMR. Contrary to existing tree-based AMR frameworks that focus on hypercubes, t8code extends the idea of using discrete space-filling curves to general element types, including prisms, pyramids and simplices. Additionally, it also supports hybrid meshes with different shapes in the same mesh. A modular approach allows to enhance t8code with additional features such as anisotropic (“2,5D”) refinement (currently work in progress) and geometric flexibility. Both of which are applied in earth system modelling. Scaling to more than one trillion mesh elements and one million parallel processes t8code is a scalable and performant alternative to unstructured meshing codes. We present the mathematical basis for tree-structured refinement, t8code’s design principles and show performance result that demonstrate its effectiveness and scalability.

High-order discontinuous Galerkin (DG) methods offer the same level of accuracy as traditional methods while using fewer degrees of freedom. At the same time, their increase in arithmetic complexity occurs locally, leading to efficient algorithms with good scalability and throughput, even on modern GPUs. In this talk we present our current efforts in developing a novel, exascale-ready dynamical core for weather and climate simulations, in which a DG scheme provides increased accuracy and performance and supports efficient utilization of next generation supercomputing hardware. Our approach is based on the flow solver Trixi.jl, which is built around a state-of-the-art spectral element method with entropy conserving flux differencing for improved robustness and with adaptive mesh refinement for reduced time-to-solution. Written in the modern high level language Julia, Trixi.jl provides rapid prototyping capabilities, HPC-grade scalability, and vendor-agnostic GPU support. Legacy applications can utilize our methods via our interface library libtrixi, which provides APIs in C and Fortran. We will present results of simulations steered by the Fortran code MESSy and show performance analyses of our CPU and GPU codes.

The storage requirements for meteorological reanalysis data have increased significantly in recent years. To address the challenges of handling these large data sets, efficient compression techniques are required. In addition, the error of the compressed data should be as small as possible. Although lossless compression algorithms exist, the resulting data are still too large. Conversely, lossy compression formats allow a small file size, but are often not able to control the error relative to the original data. We propose a multiresolution-based grid adaptation as an alternative method for lossy compression. To do this, we perform a multiresolution analysis using multiwavelets on ahierarchy of nested grids. This method provides us with local information on the differences between successive refinement levels. Since smooth regions have small local differences, we apply hard thresholding to resolve these regions on a coarser grid. Thus, the data is projected onto an adaptive grid where only regions with steep gradients or discontinuities have a high resolution, which significantly reduces the file size. We present how data compression is achieved by applying multiresolution-based grid adaptation using ERA5 meteorological reanalysis data. We additionally discuss the implementation of this method into the Lagrangian model for Massive-Parallel Trajectory Calculation (MPTRAC).

In this contribution to the mini symposium on“Dynamic adaptive scalable methods in Earth system modeling” we discuss the challenges and potential benefits of adaptive meshes in Earth system models considering two applications. Firstly, MESSy, the Modular Earth Submodel System, is a software framework used for global and regional chemistry-climate modeling. For this application AMR methods are of potential interest since several 100 to 1000 of chemical tracers increase the memory and runtime requirements compared to general circulation models by at least a factor 10. As a step towards a full AMR chemistry-climate model simulation, MESSy was connected to the AMR library t8code and the flow solver Trixi.jl. An evaluation of the integration will be shown based on an idealized flow test case. Second, SERGHEI (Simulation EnviRonment for Geomorphology, Hydrodynamics, and Ecohydrology in Integrated form) is a multi-dimensional, multi-domain, and multi-physics model framework. Its shallow-water component is used for hydrological and environmental hydrodynamic simulations and is currently exploring AMR. We describe the implementation and the implications it has in the design of SERGHEI, as well as preliminary results of AMR applied to shallow water problems.