With the advent of Computer Algebra System (CAS) such as Mathematica [1], challenging symbolic longhand calcula-tions can effectively be performed free of error and at ease. Mathematica’s integrated features allow th...With the advent of Computer Algebra System (CAS) such as Mathematica [1], challenging symbolic longhand calcula-tions can effectively be performed free of error and at ease. Mathematica’s integrated features allow the investigator to combine the needed symbolic, numeric and graphic modules all in one interactive environment. This assists the author to focus on interpreting the output rather than exerting the efforts of relating the scattered separate modules. In this note the author, utilizing these three features, explores the magneto-static field and its associated vector potential of a steady looping current. In particular by deploying the numeric features of Mathematica the exact value of the vector potential of the looping current conducive to its 3D graph is presented.展开更多
The multiscale finite element method(MsFEM)combined with conventional finite element method(CFEM)is proposed to solve static magnetic field in the ribbon magnetic core with non-periodical corners considered.Firstly,a ...The multiscale finite element method(MsFEM)combined with conventional finite element method(CFEM)is proposed to solve static magnetic field in the ribbon magnetic core with non-periodical corners considered.Firstly,a simple 2-dimensional electrostatic problem is used to introduce the MsFEM implementation process.The results are compared to analytical method,as well as conventional FEM.Then,an exam-ple of magneto-static problem is considered for a ribbon magnetic core built sheet by sheet as well as corners taken into considera-tion.Conventional FEM and MsFEM are used to compute the magneto-static field by adopting scalar magnetic potential.Both magnetic potential and magnetic flux density on a certain path are compared.It is shown that the results obtained by MsFEM agree well with the one from conventional FEM.Moreover,MsFEM combined with FEM is potentially a general strategy for mul-tiscale modeling of ribbon magnetic cores with complex and non-periodical structures considered,like corners and T-joints,which can effectively reduce the computational cost.展开更多
文摘With the advent of Computer Algebra System (CAS) such as Mathematica [1], challenging symbolic longhand calcula-tions can effectively be performed free of error and at ease. Mathematica’s integrated features allow the investigator to combine the needed symbolic, numeric and graphic modules all in one interactive environment. This assists the author to focus on interpreting the output rather than exerting the efforts of relating the scattered separate modules. In this note the author, utilizing these three features, explores the magneto-static field and its associated vector potential of a steady looping current. In particular by deploying the numeric features of Mathematica the exact value of the vector potential of the looping current conducive to its 3D graph is presented.
基金supported by the National Science Foundation of China(19934003)the State Key Project of Fundamental Research ofChina(001CB610604)the Nature Science Foundation of the Anhui Higher Education Institutions of China(2006KJ266B,ZD2007003-1)
文摘The multiscale finite element method(MsFEM)combined with conventional finite element method(CFEM)is proposed to solve static magnetic field in the ribbon magnetic core with non-periodical corners considered.Firstly,a simple 2-dimensional electrostatic problem is used to introduce the MsFEM implementation process.The results are compared to analytical method,as well as conventional FEM.Then,an exam-ple of magneto-static problem is considered for a ribbon magnetic core built sheet by sheet as well as corners taken into considera-tion.Conventional FEM and MsFEM are used to compute the magneto-static field by adopting scalar magnetic potential.Both magnetic potential and magnetic flux density on a certain path are compared.It is shown that the results obtained by MsFEM agree well with the one from conventional FEM.Moreover,MsFEM combined with FEM is potentially a general strategy for mul-tiscale modeling of ribbon magnetic cores with complex and non-periodical structures considered,like corners and T-joints,which can effectively reduce the computational cost.
