Magnetic body simulation device, micro-magnetization calculation method, and non-transitory computer-readable recording medium having stored therein a program
A magnetic body simulation device includes a memory; and a processor coupled to the memory and the processor configured to decide a search section for searching a rotational coefficient of each magnetization vector in a plurality of elements included in a magnetic body, in a process of calculating the each rotational coefficient in a state in which magnetic energy of the magnetic body is minimized, to determine whether or not a first condition is satisfied in which a width of the decided search section is less than or equal to a certain length, and a first rotational coefficient decided by a predetermined method is included in the search section, and to calculate, when the first condition is satisfied, a static magnetic field vector corresponding to the first rotational coefficient by linear interpolation based on static magnetic field vectors at both ends of the search section.
1. A magnetic body simulation device comprising:
a memory; and
a processor coupled to the memory and the processor configured to,
decide a search section for searching a minimum rotational coefficient of magnetization vectors in which magnetic energy of a magnetic body including a plurality of elements which is obtained by dividing the magnetic body is minimized based on magnetization vectors of the plurality of elements,
determine a rotational coefficient candidate by a bisection method or a secant method,
determine whether or not a width of the search section is less than or equal to a threshold value, and the rotational coefficient candidate is included in the search section,
calculate, when determining that the width is less than or equal to the threshold value and the rotational coefficient candidate is included in the search section, a static magnetic field vector corresponding to the rotational coefficient candidate by linear interpolation based on static magnetic field vectors at both ends of the search section,
calculate, based on the static magnetic field vector, the magnetic energy of the magnetic body corresponding to the rotational coefficient candidate and a differential value of the magnetic energy, and
determine whether or not the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy a Wolfe condition regarding a rotational coefficient, and
set the rotational coefficient candidate as the minimum rotational coefficient when the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy the Wolfe condition regarding the rotational coefficient.
2. The magnetic body simulation device according to claim 1 , wherein the processor is configured to calculate the calculated static magnetic field vector based on the magnetization vectors of the plurality of elements when determining that the width is larger than the threshold value or the rotational coefficient candidate is not included in the search section.
3. The magnetic body simulation device according to claim 2 , wherein the processor is configured to calculate the static magnetic field vector by using a static magnetic field potential calculated based on each magnetization vector of the plurality of elements.
4. The magnetic body simulation device according to claim 1 , wherein:
the linear interpolation is performed by dividing a sum of a first vector and a second vector by a value which is obtained by subtracting a start rotational coefficient with respect to a start point of the search section from an end rotational coefficient with respect to an end point of the search section,
the first vector is a vector which is obtained by multiplying the rotational coefficient candidate by a vector obtained by subtracting an end static magnetic field vector with respect to the end point of the search section from a start static magnetic field vector with respect to the start point of the search section,
the second vector is a vector which is obtained by subtracting a third vector from a fourth vector,
the third vector is obtained by multiplying the end static magnetic field vector by the start rotational coefficient, and
the fourth vector is obtained by multiplying the start static magnetic field vector by the end rotational coefficient.
5. The magnetic body simulation device according to claim 1 , wherein the Wolfe condition regarding the rotational coefficient is expressed by the following expression:
E (α) −E (0)≤δα E′ (α)
E (α) ≥σE′ (α)
0<δ≤σ<1,
where α is the rotational coefficient candidate, δ is a parameter which determines an upper limit of α satisfying the Wolfe condition, and σ is a parameter which determines a lower limit of α satisfying the Wolfe condition.
6. A micro-magnetization calculation method comprising:
deciding, by a processor, a search section for searching a minimum rotational coefficient of magnetization vectors in which magnetic energy of a magnetic body including a plurality of elements which is obtained by dividing the magnetic body is minimized based on magnetization vectors of the plurality of elements;
determining a rotational coefficient candidate by a bisection method or a secant method;
determining whether or not a width of the decided search section is less than or equal to a threshold value, and the rotational coefficient candidate is included in the search section;
calculating, when determining that the width is less than or equal to the threshold value and the rotational coefficient candidate is included in the search section, a static magnetic field vector corresponding to the rotational coefficient candidate by linear interpolation based on static magnetic field vectors at both ends of the search section,
calculating, based on the static magnetic field vector, the magnetic energy of the magnetic body corresponding to the rotational coefficient candidate and a differential value of the magnetic energy, and
determining whether or not the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy a Wolfe condition regarding a rotational coefficient, and
setting the rotational coefficient candidate as the minimum rotational coefficient when the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy the Wolfe condition regarding the rotational coefficient.
7. The micro-magnetization calculation method according to claim 6 , further comprising:
calculating the calculated static magnetic field vector based on the magnetization vectors of the plurality of elements when determining that the width is larger than the threshold value or the rotational coefficient candidate is not included in the search section.
8. The micro-magnetization calculation method according to claim 6 , wherein the static magnetic field vector is calculated by using a static magnetic field potential calculated based on each magnetization vector of the plurality of elements.
9. The micro-magnetization calculation method according to claim 6 , wherein:
the linear interpolation is performed by dividing a sum of a first vector and a second vector by a value which is obtained by subtracting a start rotational coefficient with respect to a start point of the search section from an end rotational coefficient with respect to an end point of the search section,
the first vector is a vector which is obtained by multiplying the rotational coefficient candidate by a vector obtained by subtracting an end static magnetic field vector with respect to the end point of the search section from a start static magnetic field vector with respect to the start point of the search section,
the second vector is a vector which is obtained by subtracting a third vector from a fourth vector,
the third vector is obtained by multiplying the end static magnetic field vector by the start rotational coefficient, and
the fourth vector is obtained by multiplying the start static magnetic field vector by the end rotational coefficient.
10. The micro-magnetization calculation method according to claim 6 , wherein the Wolfe condition regarding the rotational coefficient is expressed by the following expression:
E (α) −E (0) ≤δαE′ (α)
E (α) ≥σE′ (α)
0<δ≤σ<1,
where α is the rotational coefficient candidate, δ is a parameter which determines an upper limit of α satisfying the Wolfe condition, and σ is a parameter which determines a lower limit of α satisfying the Wolfe condition.
11. A non-transitory computer-readable recording medium having stored therein a program for causing a computer to execute a process for a simulation of a magnetic body, the process comprising:
deciding a search section for searching a minimum rotational coefficient of magnetization vectors in which magnetic energy of a magnetic body including a plurality of elements which is obtained by dividing the magnetic body is minimized based on magnetization vectors of the plurality of elements;
determining a rotational coefficient candidate by a bisection method or a secant method,
determining whether or not a width of the search section is less than or equal to a threshold value, and the rotational coefficient candidate is included in the search section;
calculating, when determining that the width is less than or equal to the threshold value and the rotational coefficient candidate is included in the search section, a static magnetic field vector corresponding to the rotational coefficient candidate by linear interpolation based on static magnetic field vectors at both ends of the search section,
calculating, based on the static magnetic field vector, the magnetic energy of the magnetic body corresponding to the rotational coefficient candidate and a differential value of the magnetic energy, and
determining whether or not the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy a Wolfe condition regarding a rotational coefficient, and
setting the rotational coefficient candidate as the minimum rotational coefficient when the calculated magnetic energy and the calculated differential value of the magnetic energy satisfy the Wolfe condition regarding the rotational coefficient.
12. The non-transitory computer-readable recording medium according to claim 11 , further comprising:
calculating the calculated static magnetic field vector based on the magnetization vectors of the plurality of elements when determining that the width is larger than the threshold value or the rotational coefficient candidate is not included in the search section.
13. The non-transitory computer-readable recording medium according to claim 12 , wherein the static magnetic field vector is calculated by using a static magnetic field potential calculated based on each magnetization vector of the plurality of elements.
14. The non-transitory computer-readable recording medium according to claim 11 , wherein:
the linear interpolation is performed by dividing a sum of a first vector and a second vector by a value which is obtained by subtracting a start rotational coefficient with respect to a start point of the search section from an end rotational coefficient with respect to an end point of the search section,
the first vector is a vector which is obtained by multiplying the rotational coefficient candidate by a vector obtained by subtracting an end static magnetic field vector with respect to the end point of the search section from a start static magnetic field vector with respect to the start point of the search section,
the second vector is a vector which is obtained by subtracting a third vector from a fourth vector,
the third vector is obtained by multiplying the end static magnetic field vector by the start rotational coefficient, and
the fourth vector is obtained by multiplying the start static magnetic field vector by the end rotational coefficient.
15. The non-transitory computer-readable recording medium according to claim 11 , wherein the Wolfe condition regarding the rotational coefficient is expressed by the following expression:
E (α) −E (0) ≤δαE′ (α)
E (α) ≥σE′ (α)
0<δ≤σ<1,
where α is the rotational coefficient candidate, δ is a parameter which determines an upper limit of α satisfying the Wolfe condition, and σ is a parameter which determines a lower limit of α satisfying the Wolfe condition.