We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.

中文翻译：

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单次和多次回弹技术，用于厚棱柱形网格层的构建和控制

我们建议一种用于构造半结构厚的棱柱形网格层的算法，该算法可确保在所得层中不存在倒置的棱柱形单元，并允许人们控制近表面网格的正交性。初始网格被建模为由超弹性材料制成的高度压缩的棱镜的薄层，该棱镜粘贴到三角化的表面上。为了计算曲面网格顶点处的鲁棒法线，我们使用基于最近球概念的二次规划算法。这种预应力材料可能会自我渗透并膨胀到计算域外部，直到达到目标层厚度为止。基于静态回弹问题的求解，提出了一种特殊的预处理松弛程序。结果表明，预处理器可以处理非常棘手的问题。一旦构建了偏移的棱柱网格，就可以使用迭代棱柱切割程序消除自相交。接下来，应用变分前进前部程序对边界附近的棱柱层进行细化和精确正交化。我们证明，从某种意义上说，所得的网格层“几乎与网格无关”，因为该层的厚度和形状对网格分辨率和三角形质量的依赖性很弱。可以逐层依次应用弹性回弹技术。我们在网格质量，局部变化问题的刚度以及网格正交性和/或层厚度平衡方面比较了单回弹技术和多回弹技术。变分超前程序用于边界层附近棱镜层的细化和精确正交化。我们证明，从某种意义上说，所得的网格层“几乎与网格无关”，因为该层的厚度和形状对网格分辨率和三角形质量的依赖性很弱。可以逐层依次应用弹性回弹技术。我们在网格质量，局部变化问题的刚度以及网格正交性和/或层厚度平衡方面比较了单回弹技术和多回弹技术。变分超前程序用于边界层附近棱镜层的细化和精确正交化。我们证明，从某种意义上说，所得的网格层“几乎与网格无关”，因为该层的厚度和形状对网格分辨率和三角形质量的依赖性很弱。可以逐层依次应用弹性回弹技术。我们在网格质量，局部变化问题的刚度以及网格正交性和/或层厚度平衡方面比较了单回弹技术和多回弹技术。我们证明，从某种意义上说，所得的网格层“几乎与网格无关”，因为该层的厚度和形状对网格分辨率和三角形质量的依赖性很弱。可以逐层依次应用弹性回弹技术。我们在网格质量，局部变化问题的刚度以及网格正交性和/或层厚度平衡方面比较了单回弹技术和多回弹技术。我们证明，从某种意义上说，所得的网格层“几乎与网格无关”，因为该层的厚度和形状对网格分辨率和三角形质量的依赖性很弱。可以逐层依次应用弹性回弹技术。我们在网格质量，局部变化问题的刚度以及网格正交性和/或层厚度平衡方面比较了单回弹技术和多回弹技术。