A domain decomposition technique combined with an enhanced geometry mapping based on the use of NURBS is considered for solving parametrized models in complex geometries (non simply connected) within the so-called proper generalized decomposition (PGD) framework, enabling the expression of the solution in each subdomain in a fully separated form, involving both the space and the model parameters. NURBS allow a compact and powerful domain mapping into a fully separated reference geometry, while the PGD allows recovering an affine structure of the problem in the reference domain, facilitating the use of the standard PGD solver for computing the parametric solution in each subdomain first, and then by enforcing the interface transmission conditions, in the whole domain.

中文翻译：

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涉及子域可分离空间表示的域分解，用于解决复杂几何中的参数问题

考虑使用基于 NURBS 的域分解技术与增强的几何映射相结合，以在所谓的适当广义分解 (PGD) 框架内求解复杂几何（非简单连接）中的参数化模型，使解决方案能够表达为每个子域都采用完全分离的形式，涉及空间和模型参数。NURBS 允许将紧凑而强大的域映射到完全分离的参考几何，而 PGD 允许在参考域中恢复问题的仿射结构，便于使用标准 PGD 求解器首先计算每个子域中的参数解，并且然后通过在整个域中强制执行接口传输条件。