To generate a mesh in a physical domain, an initial mesh of a polygonal domain that approximates the physical domain is introduced. The initial mesh is formed by using a Body Centered Cubic (BCC) lattice that can give a more efficient node ordering for the matrix vector multiplication. An optimization problem is then considered for the displacement on the initial mesh points, which maintains a good quality of triangles while aiming at fitting the initial mesh to the boundary of the physical domain. In the optimization problem, a mesh quality function is employed. The Fréchet derivative of the objective function vanishes at the optimal solution and it gives a resulting nonlinear algebraic system for the optimal solution. The nonlinear algebraic system can be solved by using the Picard or Newton method. To resolve the complexity in the physical domain, a very fine initial mesh is often required but the solution time for the nonlinear algebraic system becomes problematic. To overcome this limitation, adaptively refined grid cells for the initial BCC mesh can be used and iterative solvers combined with a domain decomposition preconditioner can be used for solving the algebraic system in the Picard or Newton method. The use of iterative solvers with a domain decomposition preconditioner gives a parallel meshing algorithm that makes the proposed scheme more efficient for large scale problems. Numerical results for various test models are included.

为了在物理域中生成网格，引入了近似物理域的多边形域的初始网格。初始网格是通过使用“体心立方”（BCC）网格形成的，该网格可以为矩阵矢量乘法提供更有效的节点排序。然后考虑针对初始网格点的位移的优化问题，该问题在将初始网格拟合到物理域的边界的同时保持了良好的三角形质量。在优化问题中，采用了网格质量函数。目标函数的Fréchet导数在最优解中消失，并且给出了最终解的非线性代数系统。非线性代数系统可以使用Picard或Newton方法求解。为了解决物理领域的复杂性，通常需要非常精细的初始网格，但是非线性代数系统的求解时间变得成问题。为了克服此限制，可以使用针对初始BCC网格的自适应精炼网格单元，并且可以将与域分解预处理器组合的迭代求解器用于以Picard或Newton方法求解代数系统。带有域分解前置条件的迭代求解器的使用给出了并行网格划分算法，该算法使所提出的方案对于大规模问题更加有效。包括各种测试模型的数值结果。可以使用针对初始BCC网格的自适应精炼网格单元，并且可以将迭代求解器与域分解预处理器结合使用，以用Picard或Newton方法求解代数系统。带有域分解前置条件的迭代求解器的使用给出了并行网格划分算法，该算法使所提出的方案对于大规模问题更加有效。包括各种测试模型的数值结果。可以使用针对初始BCC网格的自适应精炼网格单元，并且可以将迭代求解器与域分解预处理器结合使用，以用Picard或Newton方法求解代数系统。带有域分解前置条件的迭代求解器的使用给出了并行网格划分算法，该算法使所提出的方案对于大规模问题更加有效。包括各种测试模型的数值结果。