ONELAB源码解读：Cal_FemGlobalEquation – 欧菲博客

ONELAB源码解读：Cal_FemGlobalEquation

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getDP的核心算法在kernal文件夹下，在treatment_formulation.cpp中有对有限元方程的计算函数Cal_FemGlobalEquation：

void  Cal_FemGlobalEquation(struct EquationTerm    * EquationTerm_P,
			    struct DefineQuantity  * DefineQuantity_P0,
			    struct QuantityStorage * QuantityStorage_P0)

dof{}，花括号里的内容是指“未知量”的意思。见getDP官方解释：

Defines a vector of discrete quantities (vector of Degrees of freedom), to be used only in Equation terms of formulations to define (elementary) matrices. Roughly said, the Dof symbol in front of a discrete quantity indicates that this quantity is an unknown quantity, and should therefore not be considered as already computed.

在waveguide例子中formulation.pro中定义了三维有限元的方程：

Formulation {
  { Name eFormulation ; Type FemEquation ;
    Quantity {
      { Name e ; Type Local ; NameOfSpace eSpace ; }
    }
    Equation {
      Galerkin { [ (1/muR[]) * Dof{d e} , {d e} ] ;
                 In Domain ; Integration I1 ; Jacobian Jac ; }
               Galerkin { [ -k0^2 * epsR[] * Dof{e}, {e} ] ;
                 In Domain ; Integration I1 ; Jacobian Jac ; }

//      Galerkin { [ Normal[] /\ ( (1/muR[]) * Dof{d e} ) , {e} ] ;
//                 In BndABC ; Integration I1 ; Jacobian Jac ; }

      Galerkin { [ -2*I[]*k0 * (1/muR[]) * Normal[] /\ ( Normal[] /\ eInc[] ) , {e} ] ;
                 In BndABC ; Integration I1 ; Jacobian Jac ; }
      Galerkin { [ I[]*k0 * (1/muR[]) * Normal[] /\ ( Normal[] /\ Dof{e} ) , {e} ] ;
                 In BndABC ; Integration I1 ; Jacobian Jac ; }
    }
  }
  { Name hFormulation ; Type FemEquation ;
    Quantity {
      { Name h ; Type Local ; NameOfSpace hSpace ; }
    }
    Equation {
      Galerkin { [ (1/epsR[]) * Dof{d h} , {d h} ] ;
                 In Domain ; Integration I1 ; Jacobian Jac ; }
      Galerkin { [ -k0^2 * muR[] * Dof{h} , {h} ] ;
                 In Domain ; Integration I1 ; Jacobian Jac ; }

      Galerkin { [ -2*I[]*k0 * (1/epsR[]) * Normal[] /\ ( Normal[] /\ hInc[] ) , {h} ] ;
                 In BndABC ; Integration I1 ; Jacobian Jac ; }
      Galerkin { [ I[]*k0 * (1/epsR[]) * Normal[] /\ ( Normal[] /\ Dof{h} ) , {h} ] ;
                 In BndABC ; Integration I1 ; Jacobian Jac ; }
    }
  }

这里，/\代表叉积，从上面的代码可以看出，ONELAB直接将矢量波动方程搬上来了。结合《电磁场有限元方法》（金建铭）的三维有限元分析得出初步结论。ONELAB算有限元电磁场，会比专业软件慢，因为对公式进行针对性化简的过程，例如保留叉积就会增加很多计算量，而这个叉积实际上是不必要算的，见书5.3小节。

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