Control method, controller, recording medium recording control program, numerical calculation method, numerial calculator and recording medium recording numerical calculation program
AssigneesKazuo Kikuchi, VINAS Co., Ltd.
InventorsAtsuhiro Tamura, Kazuo Kikuchi, Akihiro Ida
Life of this patent
Estimating the term…
Abstract
A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by a physical quantity U, is solved by successive approximation. In calculation, (f−A·Um−B(Um)) is given as a nonlinear residual rr of an approximate solution Um, wherein m is the number of repeating times, and the approximate solution Um is repeatedly corrected so as to reduce a norm of a nonlinear residual rm+1 employed in a subsequent step.
Claims8
A method for controlling a physical quantity U, comprising:
- a step of solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- wherein (f−A·Um−B(Um)) is given as a nonlinear residual rm of an approximate solution Um, wherein m is the number of repeating times, and
- said approximate solution Um is corrected so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
A controller for controlling a physical quantity U, comprising:
- means for solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- wherein (f−A·Um−B(Um)) is given as a nonlinear residual rm of an approximate solution Um, wherein m is the number of repeating times, and
- said approximate solution Um is corrected so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
A recording medium in which a control program for allowing a computer to control a physical quantity U is recorded, said program allowing said computer to execute:
- a processing for solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- a processing for giving (f−A·Um−B(Um)) as a nonlinear residual rm of an approximate solution Um, wherein m is the number of repeating times, and
- a processing for correcting said approximate solution Um so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
A method for numerically calculating a physical quantity U, comprising:
- a step of solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- wherein (f−A·Um−B(Um)) is given as a nonlinear residual rr of an approximate solution Um, wherein m is the number of repeating times, and
- said approximate solution Um is corrected so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
A numerical calculator for calculating a physical quantity U, comprising:
- means for solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- wherein (f−A·Um−B(Um)) is given as a nonlinear residual rm of an approximate solution Um, wherein m is the number of repeating times, and
- said approximate solution Um is corrected so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
A recording medium in which a numerical calculation program for allowing a computer to numerically calculate a physical quantity U, said numerical calculation program allowing said computer to execute:
- a processing for solving, by successive approximation, A·U+B(U)=f, wherein A is a linear differential operator, B is a nonlinear differential operator, and f is an inhomogeneous term (source term) in a nonlinear partial differential equation to be satisfied by said physical quantity U,
- a processing for giving (f−A·Um−B(Um)) as a nonlinear residual rr of an approximate solution Um, wherein m is the number of repeating times, and
- a processing for correcting said approximate solution Um so as to reduce a nonlinear residual rm+1 employed in a subsequent step.
Dependencies are inferred from the claim text.