Domain Decomposition

Domain decomposition is a computational technique that divides a complex problem into smaller, more manageable subproblems, solved independently and then recombined. Current research focuses on integrating domain decomposition with various machine learning architectures, such as Physics-Informed Neural Networks (PINNs), convolutional neural networks (CNNs), and graph neural networks (GNNs), to improve the efficiency and scalability of solving partial differential equations (PDEs). This approach offers significant advantages in tackling large-scale simulations and complex geometries, leading to faster and more accurate solutions across diverse scientific and engineering applications, including fluid dynamics, heat transfer, and gravitational wave modeling. The development of efficient coupling strategies and optimized algorithms for handling subdomain interfaces remains a key area of investigation.