Structural Optimization and Parallel Computation

提出的研究将在涉及有限元分析(FEA)的无约束结构优化问题中利用并行性。典型的工程问题涉及大型有限元模型，优化算法需要数百次迭代。并行有限元分析和优化不能分离，因为梯度的计算与函数求值(FEA)密切相关，需要在处理器之间适当地分布数据，例如全局刚度矩阵和位移解。由于总的计算成本由函数求值的成本主导，因此可能更倾向于在每次迭代中以更多的线性代数运算为代价来产生更少的函数求值的方法。这可能需要计算二阶导数，以获得更好的二次型模型。将考虑线弹性有限元分析的并行化以及一阶和/或二阶导数的并行计算。在生物力学领域，研究人员正在使用最优化方法来预测由于人工假体的存在而导致的材料特性在人体股骨中的分布。目前已经提出了几种理论模型。一个典型的模型会将骨重建描述为一个优化问题，其中目标函数是应变能，自变量是每个有限元中的材料特性。并行结构优化将被用来解决这一领域的一些问题。

The proposed research will exploit parallelism in unconstrained structural optimization problems involving Finite Element Analysis (FEA). Typical engineering problems involve large finite element models and optimization algorithms take several hundred iterations. Parallel finite element analysis and optimization cannot be decoupled because calculation of gradients is closely tied with the function evaluation (FEA), requiring proper distribution of data such as global stiffness matrix and displacement solution across processors. Since the total computational cost is dominated by the cost of function evaluation, methods that result in fewer function evaluations at the expense of more linear algebraic operations per iteration might be preferred. This might require the calculation of second derivatives in order to obtain a better quadratic model. The parallelization of linear elastic finite element analysis and parallel calculation of first and/or second derivatives will be considered. In the area of biomechanics, researchers are using optimization methods to predict the distribution of material properties in the human femur due to the presence of artificial implants. Several theoretical models have been proposed. A typical model would formulate bone remodeling as an optimization problem where the objective function is strain energy and the independent variables are the material properties in each finite element. Parallel structural optimization will be used to solve some problems in this field.