In this paper, a deep learning framework combined with isogeometric analysis (IGA for short) called IGA-Reuse-Net is proposed for efficient reuse of numerical simulation on a set of topology-consistent models. Compared with previous data-driven numerical simulation methods only for simple computational domains, our method can predict high-accuracy PDE solutions over topology-consistent geometries with complex boundaries. UNet3+ architecture with interlaced sparse self-attention (ISSA) module is used to enhance the performance of the network. In addition, we propose a new loss function that combines a coefficients loss and a numerical solution loss. Several training datasets with topology-consistent models are constructed for the proposed framework. To verify the effectiveness of our approach, two different types of Poisson equations with different source functions are solved on three datasets with different topologies. Our framework can achieve a good trade-off between accuracy and efficiency. It outperforms the physics-informed neural network (PINN for short) model and yields promising results of prediction.

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bézier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.