US 6,606,586 B1Granted

Simulation method

AssigneeMitsubishi Denki Kabushiki Kaisha

InventorKiyoshi Ishikawa

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Abstract

A physical quantity at a given position in an analysis space is expressed by using a Poisson's equation, a Green's function and the Green's theorem. The equation thus obtained is substituted into an unknown parameter in the equation, to be expanded into infinite series. Stopping the expansion when the equation is expanded to some degree, the equation can be expressed only with known parameters such as boundary conditions. Through calculating the respective values of integrations included in terms of the series by the Monte Carlo method and adding them up, a physical quantity at a given position can be thereby obtained. Further, by the same method, a parasitic element constant at a given position in the analysis space can be also obtained. With this method, a simulation is achieved for obtaining a physical quantity and a parasitic element constant at a given position in an analysis space, without solving a matrix equation.

Claims19

Dependent claims

A computer simulation method for obtaining a physical quantity at a position in an electrical element, comprising the steps of:

(a) expressing a first function representing a first physical quantity satisfying a Poisson's equation with respect to a first variable indicating a given position in an analysis space of said electrical element, said analysis space comprising at least one region having a boundary comprising information on position and boundary condition
in a form of a first integral with
a difference as a first integrand
between a product of a second function representing said first physical quantity with respect to a second variable indicating a position on said boundary and a first derivative representing a normal component on said boundary out of a differentiated result of a first Green's function on said first and second variables and said first physical quantity with respect to said second variable
and a product of said first Green's function and a second derivative representing a normal component on said boundary out of a differentiated result of said second function with respect to said second variable,
said boundary as a first integral region, and
said second variable as a first variable of integration;
and
(b) substituting said first integral sequentially into either one of said second function and said second derivative that is not given as said boundary condition while updating said first variable of integration so as to provide a computer simulation to obtain said physical quantity at said given position in said analysis space of said electrical element by using said boundary condition based on a distribution of said first physical quantity.

6 more elements

A computer simulation method for obtaining a parasitic element constant in an electrical element, comprising the steps of:

(a) expressing a first function representing a first physical quantity satisfying a Poisson's equation with respect to a first variable indicating a given position in an analysis space of said electrical element, said analysis space comprising at least one region having a boundary comprising information on position and boundary condition
in a form of a first integral with
a difference as a first integrand
between a product of a second function representing said first physical quantity with respect to a second variable indicating a position on said boundary and a first derivative representing a normal component on said boundary out of a differentiated result of a first Green's function on said first and second variables and said first physical quantity with respect to said second variable
and a product of said first Green's function and a second derivative representing a normal component on said boundary out of a differentiated result of said second function with respect to said second variable,
said boundary as a first integral region, and
said second variable as a first variable of integration;
and
(b) substituting said first integral sequentially into either one of said second function and said second derivative that is not given as said boundary condition while updating said first variable of integration so as to provide a computer simulation to obtain said parasitic element constant in said analysis space of said electrical element by using said boundary condition based on a distribution of said first physical quantity,
said at least one region means a plurality of regions,
said method further comprising the steps of:
(c) expressing a third function representing a second physical quantity in a first region which is one of said plurality of regions
in a form of a second integral with
a product of a third derivative representing a normal component function said boundary of said first region out of a differentiated result of said first function with respect to said first variable on said boundary of said first region and a physical constant depending on a material of said first region as a second integrand,
said first variable as a second variable of integration, and
said boundary of said first region as the second integral region;
and
(d) performing said step (b) on a fourth function representing a parasitic element constant between said first region and a second region which is one of said plurality of regions obtained by differentiating said third function with respect to said second function in said second region to express said fourth function as a sum of series, and
obtaining values of first to n-th (n≧1) terms out of said sum of series by using said information on position and boundary condition that the said boundary comprises;
and
(e) adding all said values of said first to n-th terms obtained in said step (d) to numerically calculate a value of said fourth function.

18 more elements

A computer simulation method for obtaining a physical quantity at a position in an electrical element, comprising the steps of:

(a) expressing a first function representing a first physical quantity satisfying a Poisson's equation with respect to a first variable indicating a given position in an analysis space of said electrical element, said analysis space comprising at least one region having a boundary comprising information on position and boundary condition
in a form of a first integral with
a difference as a first integrand
between a product of a second function representing said first physical quantity with respect to a second variable indicating a position on said boundary and a first derivative representing a normal component on said boundary out of a differentiated result of a first Green's function on said first and second variables and said first physical quantity with respect to said second variable
and a product of said first Green's function and a second derivative representing a normal component on said boundary out of a differentiated result of said second function with respect to said second variable,
said boundary as a first integral region, and
said second variable as a first variable of integration;
and
(b) substituting said first integral sequentially into either one of said second function and said second derivative that is not given as said boundary condition while updating said first variable of integration,
said method further comprising the steps of:
(c) expressing a third function representing a second physical quantity in said region in a form of a second integral with
a product of a third derivative representing a normal component on said boundary out of a differentiated result of a first function with respect to said first variable on said boundary and a first physical constant depending on a material of said region as a second integrand,
said first variable as a second variable of integration, and
said boundary as the second integral region;
and
(d) performing said step (b) on said third function to express said third function as a first sum of series so as to provide a computer simulation to obtain said physical quantity at said given position in said analysis space of sail electrical element by using said boundary condition based on a distribution of said first physical quantity, and
obtaining values of first to p-th (p≧1) terms out of said first sum of series by using said information on position and boundary condition that the said boundary comprises;
and
(e) adding all said values of said first to p-th terms obtained in said step (d) to numerically calculate a value of said third function.

16 more elements

Dependencies are inferred from the claim text.