The integral equation-based solvers have difficulty dealing with multi-scale problems because of disparate meshing and consequently the coexistence of varied physics (i.e., ray physics, wave physics, and circuit physics). Equivalence principle algorithm (EPA), as a domain decomposition method, has shown a great potential to address some of these issues. The EPA initially divides an original large problem into smaller ones by defining appropriate enclosing surfaces, and then solves each of them independently. Later, it uses the equivalence principle to move the solutions to the surface and stitch them together to produce a solution for the original problem. This provides parallelization of the solution, flexibility for selecting the mesh strategy, its reuse, and also improved condition number of the matrix system. Despite these advantages, the error source for EPA has not been well-studied which will be partially addressed in here.