Cloud-native alternating directions solver for isogeometric analysis

Abstract

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.