NEW ADD-IN FOR ENGINEERING SIMULATIONS IN SPREADSHEETS USING HOMOTOPY CONTINUATION METHODS

 

L. Díaz-Montes, R. Barrera-Zapata, H. Jiménez-Islas

 

 

Solving models represented by non-linear equations is a common situation in engineering and can be a challenging task. Homotopy Continuation Methods have shown globally convergent behavior, capable of finding all the possible roots of algebraic systems. Based on these methods, a new Microsoft Office Excel add-in was developed, SphereSolver, aiming to enhance the ability to use this easily obtainable software as a simulation computing platform for engineering problems. SphereSolver was applied over different types of engineering models and the non-linear equations were solved successfully each time. Selected problems were solved with SphereSolver and compared with other solution tecniques, e.g., classical Newton’s method, Fixed Point homotopy or Affine Homotopy. It was observed that using SphereSolver the solution for selected problems was improved, i.e., the interval of convergence is extended massively and/or additional roots can be found. It can be concluded that SphereSolver is a new and efficient tool that can be used within Microsoft Excel for solving engineering problems where other software or traditional tools could fail or present limitations.