Partial Differential Equations (PDEs) are essential for modeling diverse physical and engineering systems in mechanical engineering and material science. Traditional numerical methods, such as the Finite Element Method (FEM), provide reliable solutions but often struggle with computational efficiency and scalability, especially for large or complex domains. Neural network-based approaches have recently emerged as promising alternatives, harnessing their ability to approximate nonlinear mappings and enhance computational speed. However, these methods are typically limited to simple domains, such as unit squares, restricting their applicability to real-world PDEs on complex geometries, where generating sufficient training data—even synthetically—remains challenging. To overcome these limitations, we introduce a resolution-independent, physics-pretrained neural operator (PPNO). Pretrained on simple domains like unit squares, the PPNO integrates with the Schwarz Alternating Method, which decomposes complex domains into overlapping subdomains. This combination enables effective PDE solutions across arbitrary geometries by leveraging the PPNO’s proficiency with simpler domains. We establish an approximation theory for the PPNO, proving its capability to accurately solve a wide range of elliptic PDEs. Numerical experiments validate this theory, demonstrating its effectiveness for complex structures governed by linear and hyper-elasticity with intricate microstructures.