Computer simulations with isogeometric analysis (IGA) have multiple applications, from phase-field modeling to tumor-growth simulations. We focus on the alternating-directions solver (ADS) algorithm, in which the matrix equation representing a computational problem is decomposed into parallel tasks following the binary and balanced structure of an elimination tree. In this paper, we explore the possibility of running large-scale IGA simulations using linear computational cost alternating direction solvers on top of modern data-parallel cloud computing frameworks. To this end, we propose a new way of decomposition of the elimination tree which makes the IGA alternating-direction solver effectively a large graph problem suitable for modern cloud-computing frameworks. On this basis, we propose a new algorithm for isogeometric analysis alternating-directions solver based on the Pregel computational model, used for large-scale graph-processing in the cloud. We implement a cloud-native solver using this algorithm in the Apache Giraph framework, and show that it can be applied for solution of challenging higher-order PDEs. We evaluate the solver in terms of various scalability models and run configurations. The results indicate linear scalability of the proposed algorithm with respect to the number of elements in the mesh.

具有等几何分析 (IGA) 的计算机模拟具有多种应用，从相场建模到肿瘤生长模拟。我们专注于交替方向求解器 (ADS) 算法，其中表示计算问题的矩阵方程按照消除树的二元平衡结构分解为并行任务。在本文中，我们探索了在现代数据并行云计算框架之上使用线性计算成本交替方向求解器运行大规模 IGA 模拟的可能性。为此，我们提出了一种新的消除树分解方法，使 IGA 交替方向求解器有效地成为适用于现代云计算框架的大图问题。以这个为基础，我们提出了一种基于 Pregel 计算模型的等几何分析交替方向求解器的新算法，用于云中的大规模图形处理。我们在 Apache Giraph 框架中使用该算法实现了一个云原生求解器，并表明它可以应用于具有挑战性的高阶 PDE 的求解。我们根据各种可扩展性模型和运行配置来评估求解器。结果表明，所提出的算法相对于网格中的元素数量具有线性可伸缩性。我们根据各种可扩展性模型和运行配置来评估求解器。结果表明，所提出的算法相对于网格中的元素数量具有线性可伸缩性。我们根据各种可扩展性模型和运行配置来评估求解器。结果表明，所提出的算法相对于网格中的元素数量具有线性可伸缩性。