Patent ID: 8483999

Claim:
In a computational environment having at least one computing system including at least one processor, a method of prototyping and testing a virtual model representing a physical system, wherein the method includes simplifying the model defined by a system of differential algebraic equations (DAEs) and not being in Hessenberg form, the method comprising: transforming on at least one computing system the DAEs into Hessenberg form defining an index and having levels from level-0 through level-r, wherein r is a variable representing a level greater than zero, the Hessenberg form including algebraic equations representing a constraint manifold, and differential equations; differentiating on at least one computing system the algebraic equations to produce bases for a normal space and a tangent space of the constraint manifold; representing derivatives on at least one computing system of level-zero differential variables as projections onto the normal space and the tangent space of the constraint manifold, and substituting the projections into the level-zero differential equations, so as to reduce the number of differential variables and algebraic variables in the model of the physical system; converting on at least one computing system the level-zero differential equations into level-1 algebraic equations by representing derivatives of the level-zero differential variables in terms of the projections onto the normal and tangent spaces; retaining on at least one computing system only the level-1 differential equations corresponding to level-1 differential variables for which level-1 algebraic equations cannot be solved; differentiating on at least one computing system the level-1 algebraic equations r−1 times, each time substituting differential equations of levels 1 through r−1, so as to obtain algebraic equations of levels 2 through r with respect to differential variables of levels 2 through r, respectively, keeping only differential equations for which algebraic equations of the corresponding level cannot be solved; differentiating on at least one computing system the level-1 algebraic equations again, substituting differential equations of levels 1 through r to generate a result, and projecting the result onto normal and tangent spaces so as to obtain level-(r+1) algebraic equations for algebraic variables and equations for the r-th derivative of the tangent projection of the derivative of level-0 differential variables, respectively; wherein the model of the physical system is simplified by reducing the index of the DAE and by reducing the number of differential variables in the model of the physical system; and wherein the simplified model of the physical system generates parameters for designing of a prototype and virtual testing effecting the physical system determined by variation of variables of the model.