Simulation methods and systems are described for topology and shape optimization of a geometrical representation of a physical object being modeled. An initial geometry of the physical object is represented. Equation data representing physical properties for portions of an initial geometry are defined. User inputs are received through a GUI for optimization settings and user selections of portions of the geometry being optimized. For topology optimization, various material properties and solver settings may be defined. For shape optimization, various solver settings and optimization objective may be defined. A discretized model is generated of the physical object. Solutions of the topology or shape optimization are generated and updated values are determined. Iterative operations are then performed for solving the topology or shape optimization objective expressions. The solutions are stored and graphical representations of the solutions may be generated.