ExaSolvers - Extreme scale solvers for coupled systems

ExaSolvers - 耦合系统的极端规模求解器

• 批准号: 230946257
• 负责人: Professor Dr. Lars Grasedyck
• 金额: --
• 依托单位: Institute of Computational Science
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/230946257?language=en
• 关键词: ExaSolvers; Extreme; scale; solvers; coupled

Exascale computers are supposed to exhibit billion way parallelism. Computing on such extreme scale needs methods which scale perfectly and have optimal complexity. This project proposal brings together several crucial aspects of extreme scale solving. First, the solver itself must be of optimal numerical complexity - a requirement becoming more and more severe with increasing problem size - and scale efficiently up to extreme scales of parallelism. Second, simulations on exascale systems will consume a lot of electric power, requiring algorithms and implementations with low power consumption. In the first project phase, we proved that multigrid scales efficiently unto the full size of the largest computers available and looks promising for even larger scales, as soon as such computers become available. We further proved that robustness can be maintained during the scaling process for relevant application problems while still maintaining optimal complexity. To further improve parallelism, we combined this approach with special methods for parallelization in time, solvers for optimization problems and for data uncertainty problems. All these areas introduce additional parallelization opportunites which have been used successfully as demonstrated in the four result papers from the project. The algorithms developed have been combined with the core multigrid solver and implemented in the software framework UG4 and have been proven effective in single examples. In the second project phase, we will extend the UG4 multigrid to a fast, scalable and robust solver for general systems of partial differential equations. We will further develop strategies for power efficiency on on high as well as on low algorithmic level. Adaptivity will be a major key to computational and power effciency. Besides the core solver parallel adaptive multigrid, we will increase parallelism by introducing full space-time multigrid into the core of UG4. We will further deepen the work on shape optimization and inverse modeling and make a general parallel tool available for this purpose. Morever, we will extend the work on uncertainty quantification by combining hierarchical Tucker tensor sampling with the core multigrid forward solver. Algorithms and implementations will be evaluated for energy efficiency in problem solving. Various application problems are used as benchmark problems. We will improve the skin permeation problem from phase one by including novel experimental results on the nano structure. We will further use systems such as density driven flow through porous media, poroelasticity, Navier-Stokes equations and structural mechanics problems as test cases for scaling and validation of the general solver strategy. With the uncertainty quantification approach, we will compute several benchmark problems and field cases for waste disposal sites. All algorithms will be implemented in our simulation framework UG4.

亿万级计算机被认为具有十亿种并行性。这种极端规模的计算需要完美扩展并具有最佳复杂性的方法。这个项目提案汇集了极端规模解决的几个关键方面。首先，求解器本身必须具有最佳的数值复杂性-随着问题规模的增加，这一要求变得越来越严格-并且可以有效地扩展到并行的极端规模。其次，在亿亿次系统上进行仿真将消耗大量电力，需要低功耗的算法和实现。在项目的第一阶段，我们证明了多重网格可以有效地扩展到最大计算机的全尺寸，并且一旦这些计算机可用，就有希望扩展到更大的规模。我们进一步证明了在相关应用问题的缩放过程中可以保持鲁棒性，同时仍然保持最佳的复杂性。为了进一步提高并行性，我们将这种方法与时间并行化的特殊方法，优化问题和数据不确定性问题的求解器相结合。所有这些领域都引入了额外的并行化机会，这些机会已在该项目的四份成果文件中得到成功使用。所开发的算法已与核心多重网格求解器相结合，并在软件框架UG 4中实现，并已在单个例子中被证明是有效的。在项目的第二阶段，我们将把UG 4多重网格扩展为一个快速、可扩展和鲁棒的偏微分方程求解器。我们将进一步开发高算法水平和低算法水平的功率效率策略。适应性将是计算和功率效率的主要关键。除了核心求解器并行自适应多重网格，我们将通过引入全时空多重网格到UG 4的核心来增加并行性。我们将进一步深化形状优化和反建模方面的工作，并为此目的提供一个通用的并行工具。此外，我们将通过将分层Tucker张量采样与核心多重网格正演求解器相结合来扩展不确定性量化的工作。算法和实现将在解决问题的能源效率进行评估。各种应用问题被用作基准问题。我们将改善皮肤渗透问题，从第一阶段，包括新的实验结果的纳米结构。我们将进一步使用系统，如密度驱动的多孔介质，多孔弹性，Navier-Stokes方程和结构力学问题作为测试用例的缩放和验证的一般求解策略。利用不确定性量化方法，我们将计算垃圾处理场的几个基准问题和现场案例。所有的算法将在我们的仿真框架UG 4中实现。