Parallel Solution of Thermomechanical Inverse Problems for Laser Dieless Drawing of Ultra-Thin Wire

Abstract

The paper discusses the solving of inverse thermomechanical problems requiring a large number of FEM tasks with various boundary conditions. The study examined the case when all tasks have the same number of nodes, finite elements, and nodal connections. In this study, the speedup of the solution of the inverse problem is achieved in two ways: 1. The solution of all FEM tasks in parallel mode. 2. The use by all FEM tasks a common matrix with addresses of nonzero elements in the stiffness matrices. These algorithms are implemented in the own FEM code, designed to solve inverse problems of the hot metal forming. The calculations showed that developed code in parallel mode is effective for the number of tasks late than 0,7-0,9 of the number of available processors. Thus, at some point, it becomes effective to use a sequential solution to all tasks and to use a common matrix of addresses of nonzero elements in the stiffness matrix. The achieved acceleration at the optimal choice of the algorithm is 2–10 times compared with the classical multivariate calculations in the FEM. The paper provides an example of the practical application of the developed code for calculating the allowable processing maps for laser dieless drawing of ultra-thin wire from copper alloy by solving the thermomechanical inverse problem. The achieved acceleration made it possible to use the developed parallel code in the control software of the laboratory setup for laser dieless drawing.