A method for engineering analysis using a regular or structured grid is described which does not require a conforming mesh to approximate the geometry of the analysis domain. The geometry of the domain is represented using implicit equations and a structured grid is used to approximate the solution. Solution structures are constructed using implicit equations such that the essential boundary conditions are satisfied exactly. The use of structured grid eliminates the need to generate a conforming mesh and thus reduces time taken to create models for analysis. This approach is used to solve boundary value problems arising in thermal and structural analysis. Convergence analysis is performed for several numerical examples and the results are compared with analytical and finite element analysis solutions to show that the method gives solutions that are similar to the finite element method in quality but is often less computationally expensive.

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