Method and apparatus for process modeling using a dynamical system
AssigneeInnovative Computing Group, Inc.
InventorOlurinde E. Lafe
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Abstract
A method and apparatus for modeling physical, chemical and sundry conceptual processes is taught. A family of multi, state dynamical systems are used to solve the differential equations that define these processes. Differential bases functions are generated from the evolving states of cellular automata. The use of the differential basis functions greatly simplifies the modeling process. The present invention avoids the use of millions of computational cells as required by the prior art.
Claims12
A system for modeling a physical process defined by a governing equation expressible in the form of at least one partial differential equation indicative of the dependence of the characteristics of the physical process on one or more independent variables, wherein the physical process is one of (a) potential flow, (b) heat conduction, (c) plate deformation, (d) vibration, (e) convective-diffusion, and (f) wave scattering, the system comprising:
- first storage means for storing first data defining a constituitive property of the material;
- second storage means for storing second data defining a physical region in which the physical process takes place;
- third storage means for storing third data defining at least one of:
- initial conditions associated with the physical process, and boundary conditions associated with the physical process;
- fourth storage means for storing fourth data defining said at least one differential equation associated with the physical process being modeled;
- rule set generation means for generating rule set parameters for a dynamical system;
- dynamical rule processing means for evolving the dynamical system using the rule set parameters;
- transform bases generation means for generating transform bases from the evolved dynamical system;
- differential transform bases generation means for generating differential transform bases by mapping transform bases into a continuous domain and performing differential operations in accordance with the at least one differential equation defined by the fourth data;
- dynamical system processing means for determining a solution matrix H in accordance with the transform bases and the differential transform bases,
- inverting means for inverting the solution matrix H to generate a solution for the differential equation defined by the fourth data, wherein said inverting means receives the third data stored in the third storage means;
- and
- output means for outputting the solution for said at least one differential equation defined by the fourth data, said solution indicative of one of:
- a potential of a potential flow process, a temperature of a heat conduction process, a deformation of a plate deformation process, a displacement of a vibration process, a pressure of a convective-diffusion process, and a wave field of a wave scattering process.
A method for modeling a physical process defined by a governing equation expressible in the form of at least one partial differential equation indicative of the dependence of the characteristics of the physical process on one or more independent variables, wherein the physical process is one of (a) potential flow, (b) heat conduction, (c) plate deformation, (d) vibration, (e) convective-diffusion, and (f) wave scattering, the method comprising:
- storing first data defining a constituitive property of the material;
- storing second data defining a physical region in which the physical process takes place;
- storing third data defining at least one of:
- initial conditions associated with the physical process, and boundary conditions associated with the physical process;
- storing fourth data defining said at least one differential equation associated with the physical process being modeled;
- generating rule set parameters for a dynamical system;
- evolving the dynamical system using the rule set parameters;
- generating transform bases from the evolved dynamical system;
- generating differential transform bases by mapping transform bases into a continuous domain and performing differential operations in accordance with the at least one differential equation;
- determining a solution matrix H in accordance with the transform bases and the differential transform bases;
- inverting the solution matrix H using said third data, to generate a solution for the differential equation;
- and
- outputting the solution for said at least one differential equation defined by the fourth data, said solution indicative of one of:
- a potential of a potential flow process, a temperature of a heat conduction process, a deformation of a plate deformation process, a displacement of a vibration process, a pressure of a convective-diffusion process, and a wave field of a wave scattering process.
Dependencies are inferred from the claim text.