Function File: S = Uscharfettergummel3 (mesh, alpha, gamma, eta, beta)

Builds the Scharfetter-Gummel matrix for the discretization of the LHS of the equation:

where:

• alpha is an element-wise constant scalar function
• eta, gamma are piecewise linear conforming scalar functions
• beta is an element-wise constant vector function

Instead of passing the vector field beta directly one can pass a piecewise linear conforming scalar function phi as the last input. In such case beta = grad phi is assumed. If phi is a single scalar value beta is assumed to be 0 in the whole domain.

Example:

          [mesh.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
          mesh = Umeshproperties(mesh);
          x = mesh.p(1,:)';
          Dnodes = Unodesonside(mesh,[2,4]);
          Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
          Varnodes = setdiff(1:Nnodes,Dnodes);
          alpha  = ones(Nelements,1); eta = .1*ones(Nnodes,1);
          beta   = [ones(1,Nelements);zeros(1,Nelements)];
          gamma  = ones(Nnodes,1);
          f      = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
          S = Uscharfettergummel3(mesh,alpha,gamma,eta,beta);
          u = zeros(Nnodes,1);
          u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
          uex = x - (exp(10*x)-1)/(exp(10)-1);
          assert(u,uex,1e-7)

See also: Ucomplap Ucompconst Ucompmass2 Uscharfettergummel