The advancement in the field of computer-aided design (CAD) and 3D printing enables the creation of devices and structures with complex geometries and multiple functionalities. As the complexity of the solid model increases, generating meshes or grids to perform structural analyses becomes challenging, resulting in inconsistency in capturing the complex shapes (topology) of the structures. In this study, we develop a stencil generator approach that enables easy discretization of structures of complex geometries consistent with the original solid models and directly solves boundary value problems within coupled partial differential equations. Thus, we can simultaneously perform the design, analysis, and fabrication of the structures using the original CAD file. We use the Stereolithography (.stl) file format to discretize structures. We present new slicing and sorting algorithms for 2D and 3D complex geometries, for stencil generations that can capture various surface topologies (e.g., rounded and sharp surfaces) of the structures. The generated stencil (nodal group) can be readily implemented within finite-difference methods to numerically solve multi-field boundary value problems. For a demonstration of the stencil generation and simulation pipeline, we present two boundary value problems on various complex geometries with different surface topologies. The first example solves the Poisson equation, which is relevant for many physical phenomena, such as heat transfer and diffusion of fluid through solid bodies. The second example simulates coupled systems of biodegradable polymer solids, which include fluid diffusion, hydrolytic attack, and erosion processes. The erosion process leads to a change in the shapes and sizes of the geometries over time.

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