Symbolic evaluation engine for high-performance simulations

A machine-readable storage medium having stored thereon machine executable instructions, the execution of said instructions adapted to implement a method of simulating a system, the method comprising:

• defining equations modeling the system using terms having characteristics encapsulated within the term;
• performing symbolic processing on the established equations for simplification;
• and
• performing system processing on the established equations for efficient simulation.

A method of symbolically processing a set of equations, comprising:

• assigning a portion of the set of equations to variables that have non-zero partial derivatives;
• differentiating the remainder of the set of equations;
• approximating an algebraic derivative for those equations that cannot by symbolically differentiated;
• symbolically integrating equations that cannot be assigned;
• differentiating equations that add output derivates and integrating equations that add output integrals;
• and
• eliminating an integral as each symbolically differentiated or integrated equation eliminates a numeric integration, such that the integral is converted to an algebraic variable by eliminating the derivative or integral relationship.

A machine-readable storage medium having stored thereon machine executable instructions, the execution of said instructions adapted to implement a method of symbolically processing a set of equations, the method comprising:

• assigning a portion of the set of equations to variables that have non-zero partial derivatives;
• differentiating the remainder of the set of equations;
• approximating an algebraic derivative for those equations that cannot by symbolically differentiated;
• symbolically integrating equations that cannot be assigned;
• differentiating equations that add output derivates and integrating equations that add output integrals;
• and
• eliminating an integral as each symbolically differentiated or integrated equation eliminates a numeric integration, such that the integral is converted to an algebraic variable by eliminating the derivative or integral relationship.

A method of eliminating an integral in a Pantelides algorithm, comprising:

• assigning a preferred integration location rank to one or more integrals;
• utilizing the preferred integration location rank, assigning integrals to equations;
• and
• eliminating the integration of assigned or solved integral variables.

A machine-readable storage medium having stored thereon machine executable instructions, the execution of said instructions adapted to implement a method of eliminating an integral in a Pantelides algorithm, the method comprising:

• assigning a preferred integration location rank to one or more integrals;
• utilizing the preferred integration location rank, assigning integrals to equations;
• and
• eliminating the integration of assigned or solved integral variables.

A method of tearing equations, comprising:

• identifying block variables in the equations in a block in which the block variables appear linearly with constant coefficients;
• determining the solvability of the nonlinear equations;
• solving nonlinear integration equations for their respective integrals;
• solving the linear equations;
• solving the nonlinear equations utilizing iterates and block variables solved from the linear equations;
• and
• scanning for solved for variables for identification of variables that are independent and may be removed from the block.

A machine-readable storage medium having stored thereon machine executable instructions, the execution of said instructions adapted to implement a method of tearing blocked equations, the method comprising:

• identifying block variables in the equations in a block in which the block variables appear linearly with constant coefficients;
• solving nonlinear integration equations for their respective integrals;
• solving the linear equations;
• determining the solvability of the nonlinear equations;
• solving the nonlinear equations utilizing iterates and block variables solved from the linear equations;
• and
• scanning for solved for variables for identification of variables that are independent and may be removed from the block.

A method of simulating a system, comprising:

• establishing equations modeling the system using terms having characteristics encapsulated within the term;
• performing symbolic processing on the established equations for reducing the number of terms in the equations;
• and
• performing system processing on the established equations for efficient simulation.

A method of simulating a component, comprising:

• establishing equations modeling the component using terms having characteristics encapsulated within the term;
• performing symbolic processing on the established equations for simplification;
• and
• performing system processing on the established equations for efficient simulation.