# doc-cache created by Octave 11.3.0
# name: cache
# type: cell
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# columns: 47
# name: <cell-element>
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# elements: 1
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bim1a_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 835
 -- Function File: [A] = bim1a_advection_diffusion(MESH,ALPHA,GAMMA,ETA,BETA)

     Build the Scharfetter-Gummel stabilized stiffness matrix for a
     diffusion-advection problem.

     The equation taken into account is:

     - div (ALPHA * GAMMA (ETA grad (u) - BETA u)) = f

     where ALPHA is an element-wise constant scalar function, ETA and 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.

     See also: bim1a_rhs, bim1a_reaction, bim1a_laplacian,
     bim2a_advection_diffusion.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-adve...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
bim1a_advection_upwind


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 611
 -- Function File: [A] = bim1a_advection_upwind (MESH, BETA)

     Build the UW stabilized stiffness matrix for an advection problem.

     The equation taken into account is:

     (BETA u)' = f

     where BETA is an element-wise constant.

     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.

     See also: bim1a_rhs, bim1a_reaction, bim1a_laplacian,
     bim2a_advection_diffusion.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Build the UW stabilized stiffness matrix for an advection problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
bim1a_axisymmetric_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1261
 -- Function File: [A] =
          bim1a_axisymmetric_advection_diffusion(MESH,ALPHA,GAMMA,ETA,BETA)

     Build the Scharfetter-Gummel stabilized stiffness matrix for a
     diffusion-advection problem in cylindrical coordinates with axisymmetric
     configuration.  Rotational symmetry is assumed with respect to be the
     vertical axis r=0.  Only grids that DO NOT contain r=0 are admissible.

             |   |-------|   OK       |-------|   |   OK        |--|-----|   NO!
            r=0                                  r=0              r=0

     The equation taken into account is:

     - 1/r * d/dr (ALPHA * GAMMA (ETA du/dr - BETA u)) = f

     where ALPHA is an element-wise constant scalar function, ETA and 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.

     See also: bim1a_axisymmetric_rhs, bim1a_axisymmetric_reaction,
     bim1a_axisymmetric_laplacian, bim2a_axisymmetric_advection_diffusion.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-adve...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
bim1a_axisymmetric_advection_upwind


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 754
 -- Function File: [A] = bim1a_axisymmetric_advection_upwind (MESH, BETA)

     Build the Upwind stabilized stiffness matrix for an advection problem in
     cylindrical coordinates with axisymmetric configuration.

     The equation taken into account is:

     1/r * (r * BETA u)' = f

     where BETA is an element-wise constant.

     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.

     See also: bim1a_axisymmetric_advection_diffusion, bim1a_axisymmetric_rhs,
     bim1a_axisymmetric_reaction, bim1a_axisymmetric_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Upwind stabilized stiffness matrix for an advection problem in
cyli...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
bim1a_axisymmetric_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 824
 -- Function File: A = bim1a_axisymmetric_laplacian (MESH,EPSILON,KAPPA)

     Build the standard finite element stiffness matrix for a diffusion problem
     in cylindrical coordinates with axisymmetric configuration.  Rotational
     symmetry is assumed with respect to be the vertical axis r=0.  Only grids
     that DO NOT contain r=0 are admissible.

             |   |-------|   OK       |--|-----|   NO!
            r=0                         r=0

     The equation taken into account is:

     - 1/r * (r * EPSILON * KAPPA ( u' ))' = f

     where EPSILON is an element-wise constant scalar function, while KAPPA is a
     piecewise linear conforming scalar function.

     See also: bim1a_axisymmetric_rhs, bim1a_axisymmetric_reaction,
     bim1a_axisymmetric_advection_diffusion, bim2a_laplacian, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the standard finite element stiffness matrix for a diffusion problem in...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
bim1a_axisymmetric_reaction


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 553
 -- Function File: [C] = bim1a_axisymmetric_reaction(MESH,DELTA,ZETA)

     Build the lumped finite element mass matrix for a diffusion problem in
     cylindrical coordinates with axisymmetric configuration.

     The equation taken into account is:

     DELTA * ZETA * u = f

     where DELTA is an element-wise constant scalar function, while ZETA is a
     piecewise linear conforming scalar function.

     See also: bim1a_axisymmetric_rhs, bim1a_axisymmetric_advection_diffusion,
     bim1a_axisymmetric_laplacian, bim2a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the lumped finite element mass matrix for a diffusion problem in
cylind...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
bim1a_axisymmetric_rhs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 445
 -- Function File: [B] = bim1a_rhs(MESH,F, G)

     Build the finite element right-hand side of a diffusion problem employing
     mass-lumping.

     The equation taken into account is:

     DELTA * u = f * g

     where F is an element-wise constant scalar function, while G is a piecewise
     linear conforming scalar function.

     See also: bim1a_reaction, bim1a_advection_diffusion, bim1a_laplacian,
     bim2a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the finite element right-hand side of a diffusion problem employing
mas...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
bim1a_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 462
 -- Function File: A = bim1a_laplacian (MESH,EPSILON,KAPPA)

     Build the standard finite element stiffness matrix for a diffusion problem.

     The equation taken into account is:

     - (EPSILON * KAPPA ( u' ))' = f

     where EPSILON is an element-wise constant scalar function, while KAPPA is a
     piecewise linear conforming scalar function.

     See also: bim1a_rhs, bim1a_reaction, bim1a_advection_diffusion,
     bim2a_laplacian, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
Build the standard finite element stiffness matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
bim1a_reaction


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 437
 -- Function File: [C] = bim1a_reaction(MESH,DELTA,ZETA)

     Build the lumped finite element mass matrix for a diffusion problem.

     The equation taken into account is:

     DELTA * ZETA * u = f

     where DELTA is an element-wise constant scalar function, while ZETA is a
     piecewise linear conforming scalar function.

     See also: bim1a_rhs, bim1a_advection_diffusion, bim1a_laplacian,
     bim2a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
Build the lumped finite element mass matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bim1a_rhs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 445
 -- Function File: [B] = bim1a_rhs(MESH,F, G)

     Build the finite element right-hand side of a diffusion problem employing
     mass-lumping.

     The equation taken into account is:

     DELTA * u = f * g

     where F is an element-wise constant scalar function, while G is a piecewise
     linear conforming scalar function.

     See also: bim1a_reaction, bim1a_advection_diffusion, bim1a_laplacian,
     bim2a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the finite element right-hand side of a diffusion problem employing
mas...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
bim1c_elem_to_nodes


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 602
 -- Function File: U_NOD = bim1c_elem_to_nodes (MESH, U_EL)
 -- Function File: U_NOD = bim1c_elem_to_nodes (M_EL, U_EL)
 -- Function File: [U_NOD, M_EL] = bim1c_elem_to_nodes ( ... )

     Compute interpolated values at nodes U_NOD given values at element
     mid-points U_EL.  If called with more than one output, also return the
     interpolation matrix M_EL such that ‘u_nod = m_el * u_el’.  If repeatedly
     performing interpolation on the same mesh the matrix M_EL obtained by a
     previous call to ‘bim1c_elem_to_nodes’ may be passed as input to avoid
     unnecessary computations.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute interpolated values at nodes U_NOD given values at element mid-points...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
bim1c_norm


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 565
 -- Function File: [NORM_U] = bim1c_norm(MESH,U,NORM_TYPE)

     Compute the NORM_TYPE-norm of function U on the domain described by the
     triangular grid MESH.

     The input function U can be either a piecewise linear conforming scalar
     function or an elementwise constant scalar or vector function.

     The string parameter NORM_TYPE can be one among 'L2', 'H1' and 'inf'.

     Should the input function be piecewise constant, the H1 norm will not be
     computed and the function will return an error message.

     See also: bim2c_norm, bim3c_norm.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the NORM_TYPE-norm of function U on the domain described by the
trian...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
bim2a_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1651
 -- Function File: [A] = bim2a_advection_diffusion(MESH,ALPHA,GAMMA,ETA,BETA)

     Build the Scharfetter-Gummel stabilized stiffness matrix for a
     diffusion-advection problem.

     The equation taken into account is:

     - div (ALPHA * GAMMA (ETA grad (u) - BETA u )) = f

     where ALPHA is an element-wise constant scalar function, ETA and 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 = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
           mesh = bim2c_mesh_properties(mesh);
           x    = mesh.p(1,:)';

           Dnodes    = bim2c_unknowns_on_side(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      = bim2a_rhs(mesh,ones(Nnodes,1),ones(Nelements,1));

           S   = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
           u   = zeros(Nnodes,1);
           uex = x - (exp(10*x)-1)/(exp(10)-1);

           u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);

           assert(u,uex,1e-7)

     See also: bim2a_rhs, bim2a_reaction, bim2c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-adve...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
bim2a_advection_upwind


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 604
 -- Function File: [A] = bim2a_advection_upwind (MESH, BETA)

     Build the UW stabilized stiffness matrix for an advection problem.

     The equation taken into account is:

     div (BETA u) = f

     where 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.

     See also: bim2a_rhs, bim2a_reaction, bim2c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Build the UW stabilized stiffness matrix for an advection problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
bim2a_axisymmetric_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1404
 -- Function File: [A] =
          bim2a_axisymmetric_advection_diffusion(MESH,ALPHA,GAMMA,ETA,BETA)

     Build the Scharfetter-Gummel stabilized stiffness matrix for a
     diffusion-advection problem in cylindrical coordinates with axisymmetric
     configuration.  Rotational symmetry is assumed with respect to be the
     vertical axis r=0.  Only plane geometries that DO NOT intersect the
     symmetry axis are admitted.

             |   ____                 _|____
             |  |    \               \ |    |
           z |  |     \  OK           \|    |   NO!
             |  |______\               |\___|
             |     r                   |

     The equation taken into account is:

     1/r * d(r * Fr)/dr + dFz/dz = f

     with

     F = [Fr, Fz]' = - ALPHA * GAMMA ( ETA grad (u) - BETA u )

     where ALPHA is an element-wise constant scalar function, ETA and 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.

     See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction,
     bim2a_advection_diffusion, bim2c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-adve...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
bim2a_axisymmetric_advection_upwind


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 787
 -- Function File: [A] = bim2a_axisymmetric_advection_upwind (MESH, BETA)

     Build the Upwind stabilized stiffness matrix for an advection problem in
     cylindrical coordinates with axisymmetric configuration.

     The equation taken into account is:

     1/r * d/dr (r * BETA_r u) + d/dz (BETA_z u) = f

     where 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.

     See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction,
     bim2a_axisymmetric_advection_diffusion, bim2c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Upwind stabilized stiffness matrix for an advection problem in
cyli...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
bim2a_axisymmetric_boundary_mass


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 645
 -- Function File: [M] =
          bim2a_axisymmetric_boundary_mass(MESH,SIDELIST,NODELIST)

     Build the lumped boundary mass matrix needed to apply Robin and Neumann
     boundary conditions in a problem in cylindrical coordinates with
     axisymmetric configuration.

     The vector SIDELIST contains the list of the side edges contributing to the
     mass matrix.

     The optional argument NODELIST contains the list of the degrees of freedom
     on the boundary.

     See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_advection_diffusion,
     bim2a_axisymmetric_laplacian, bim2a_axisymmetric_reaction,
     bim2a_boundary_mass.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the lumped boundary mass matrix needed to apply Robin and Neumann bound...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
bim2a_axisymmetric_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1057
 -- Function File: A = bim2a_axisymmetric_laplacian (MESH,EPSILON,KAPPA)

     Build the standard finite element stiffness matrix for a diffusion problem
     in cylindrical coordinates with axisymmetric configuration.  Rotational
     symmetry is assumed with respect to be the vertical axis r=0.  Only plane
     geometries that DO NOT intersect the symmetry axis are admitted.

              |   ____                 _|____
              |  |    \               \ |    |
            z |  |     \  OK           \|    |   NO!
              |  |______\               |\___|
              |     r                   |

     The equation taken into account is:

     1/r * d(r * Fr)/dr + dFz/dz = f

     with

     F = [Fr, Fz]' = - EPSILON * KAPPA grad (u)

     where EPSILON is an element-wise constant scalar function, while KAPPA is a
     piecewise linear conforming scalar function.

     See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction,
     bim2a_axisymmetric_advection_diffusion, bim2a_laplacian, bim1a_laplacian,
     bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the standard finite element stiffness matrix for a diffusion problem in...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
bim2a_axisymmetric_reaction


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 561
 -- Function File: [C] = bim2a_axisymmetric_reaction(MESH,DELTA,ZETA)

     Build the lumped finite element mass matrix for a diffusion problem in
     cylindrical coordinates with axisymmetric configuration.

     The equation taken into account is:

     DELTA * ZETA * u = f

     where DELTA is an element-wise constant scalar function, while ZETA is a
     piecewise linear conforming scalar function.

     See also: bim2a_rhs, bim2a_axisymmetric_advection_diffusion,
     bim2a_axisymmetric_laplacian, bim2a_reaction, bim1a_reaction,
     bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the lumped finite element mass matrix for a diffusion problem in
cylind...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
bim2a_axisymmetric_rhs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 557
 -- Function File: [B] = bim2a_axisymmetric_rhs(MESH,F,G)

     Build the finite element right-hand side of a diffusion problem in
     cylindrical coordinates with axisymmetric configuration employing
     mass-lumping.

     The equation taken into account is:

     DELTA * u = f * g

     where F is an element-wise constant scalar function, while G is a piecewise
     linear conforming scalar function.

     See also: bim2a_axisymmetric_reaction,
     bim2a_axisymmetric_advection_diffusion, bim2a_axisymmetric_laplacian,
     bim1a_axisymmetric_rhs.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the finite element right-hand side of a diffusion problem in cylindrica...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
bim2a_boundary_mass


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 455
 -- Function File: [M] = bim2a_boundary_mass(MESH,SIDELIST,NODELIST)

     Build the lumped boundary mass matrix needed to apply Robin boundary
     conditions.

     The vector SIDELIST contains the list of the side edges contributing to the
     mass matrix.

     The optional argument NODELIST contains the list of the degrees of freedom
     on the boundary.

     See also: bim2a_rhs, bim2a_advection_diffusion, bim2a_laplacian,
     bim2a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the lumped boundary mass matrix needed to apply Robin boundary conditio...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
bim2a_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 467
 -- Function File: A = bim2a_laplacian (MESH,EPSILON,KAPPA)

     Build the standard finite element stiffness matrix for a diffusion problem.

     The equation taken into account is:

     - div (EPSILON * KAPPA grad (u)) = f

     where EPSILON is an element-wise constant scalar function, while KAPPA is a
     piecewise linear conforming scalar function.

     See also: bim2a_rhs, bim2a_reaction, bim2a_advection_diffusion,
     bim1a_laplacian, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
Build the standard finite element stiffness matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
bim2a_reaction


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 437
 -- Function File: [C] = bim2a_reaction(MESH,DELTA,ZETA)

     Build the lumped finite element mass matrix for a diffusion problem.

     The equation taken into account is:

     DELTA * ZETA * u = f

     where DELTA is an element-wise constant scalar function, while ZETA is a
     piecewise linear conforming scalar function.

     See also: bim2a_rhs, bim2a_advection_diffusion, bim2a_laplacian,
     bim1a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
Build the lumped finite element mass matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bim2a_rhs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 444
 -- Function File: [B] = bim2a_rhs(MESH,F,G)

     Build the finite element right-hand side of a diffusion problem employing
     mass-lumping.

     The equation taken into account is:

     DELTA * u = f * g

     where F is an element-wise constant scalar function, while G is a piecewise
     linear conforming scalar function.

     See also: bim2a_reaction, bim2a_advection_diffusion, bim2a_laplacian,
     bim1a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the finite element right-hand side of a diffusion problem employing
mas...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 17
bim2c_global_flux


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 853
 -- Function File: [JX,JY] = bim2c_global_flux(MESH,U,ALPHA,GAMMA,ETA,BETA)

     Compute the flux associated with the Scharfetter-Gummel approximation of
     the scalar field U.

     The vector field is defined as:

     J(U) = ALPHA* GAMMA * (ETA * grad U - BETA * U))

     where ALPHA is an element-wise constant scalar function, ETA and GAMMA are
     piecewise linear conforming scalar functions, while BETA is element-wise
     constant vector function.

     J(U) 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.

     See also: bim2c_pde_gradient,bim2a_advection_diffusion.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the flux associated with the Scharfetter-Gummel approximation of the
...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
bim2c_intrp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 277
 -- Function File: DATA = bim2c_intrp (MSH, N_DATA, E_DATA, POINTS)

     Compute interpolated values of multicomponent node centered field N_DATA
     and/or cell centered field N_DATA at an arbitrary set of points whose
     coordinates are given in the n_by_2 matrix POINTS.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute interpolated values of multicomponent node centered field N_DATA and/...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
bim2c_mesh_properties


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 270
 -- Function File: [OMESH] = bim2c_mesh_properties(IMESH)

     Compute the properties of IMESH needed by BIM method and append them to
     OMESH as fields.

     See also: bim2a_reaction, bim2a_advection_diffusion, bim2a_rhs,
     bim2a_laplacian, bim2a_boundary_mass.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the properties of IMESH needed by BIM method and append them to OMESH...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
bim2c_norm


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 676
 -- Function File: [NORM_U] = bim2c_norm(MESH,U,NORM_TYPE)

     Compute the NORM_TYPE-norm of function U on the domain described by the
     triangular grid MESH.

     The input function U can be either a piecewise linear conforming scalar
     function or an elementwise constant scalar or vector function.

     The string parameter NORM_TYPE can be one among 'L2', 'H1' and 'inf'.

     Should the input function be piecewise constant, the H1 norm will not be
     computed and the function will return an error message.

     For the numerical integration of the L2 norm the second order middle point
     quadrature rule is used.

     See also: bim1c_norm, bim3c_norm.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the NORM_TYPE-norm of function U on the domain described by the
trian...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
bim2c_pde_gradient


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
 -- Function File: [GX,GY] = bim2c_pde_gradient(MESH,U)

     Compute the gradient of the piecewise linear conforming scalar function U.

     See also: bim2c_global_flux.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 74
Compute the gradient of the piecewise linear conforming scalar function U.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
bim2c_tri_to_nodes


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 616
 -- Function File: U_NOD = bim2c_tri_to_nodes (MESH, U_TRI)
 -- Function File: U_NOD = bim2c_tri_to_nodes (M_TRI, U_TRI)
 -- Function File: [U_NOD, M_TRI] = bim2c_tri_to_nodes ( ... )

     Compute interpolated values at triangle nodes U_NOD given values at
     triangle mid-points U_TRI.  If called with more than one output, also
     return the interpolation matrix M_TRI such that ‘u_nod = m_tri * u_tri’.
     If repeatedly performing interpolation on the same mesh the matrix M_TRI
     obtained by a previous call to ‘bim2c_tri_to_nodes’ may be passed as input
     to avoid unnecessary computations.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute interpolated values at triangle nodes U_NOD given values at triangle
...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
bim2c_unknowns_on_side


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 250
 -- Function File: [NODELIST] = bim2c_unknowns_on_side(MESH,SIDELIST)

     Return the list of the mesh nodes that lie on the geometrical sides
     specified in SIDELIST.

     See also: bim3c_unknown_on_faces, bim2c_pde_gradient, bim2c_global_flux.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return the list of the mesh nodes that lie on the geometrical sides specified...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
bim3a_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 469
 -- Function File: [A] = bim3a_advection_diffusion (MESH, ALPHA, V)

     Build the Scharfetter-Gummel stabilized stiffness matrix for a
     diffusion-advection problem.

     The equation taken into account is:

     - div (ALPHA ( grad (u) - grad (V) u)) = f

     where V is a piecewise linear continuous scalar functions and ALPHA is a
     piecewise constant scalar function.

     See also: bim3a_rhs, bim3a_reaction, bim3a_laplacian,
     bim3c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-adve...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
bim3a_boundary_mass


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 471
 -- Function File: [M] = bim3a_boundary_mass(MESH,FACELIST,NODELIST)

     Build the lumped boundary mass matrix needed to apply Robin boundary
     conditions.

     The vector FACELIST contains the list of the faces contributing to the mass
     matrix.

     The optional argument NODELIST contains the list of the degrees of freedom
     on the boundary.

     See also: bim3a_rhs, bim3a_advection_diffusion, bim3a_laplacian,
     bim3a_reaction, bim2a_boundary_mass.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the lumped boundary mass matrix needed to apply Robin boundary conditio...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
bim3a_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 432
 -- Function File: A = bim3a_laplacian (MESH, EPSILON, KAPPA)

     Build the standard finite element stiffness matrix for a diffusion problem.

     The equation taken into account is:

     - (EPSILON * KAPPA ( u' ))' = f

     where EPSILON is an element-wise constant scalar function, while KAPPA is a
     piecewise linear conforming scalar function.

     See also: bim3a_rhs, bim3a_reaction, bim2a_laplacian, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
Build the standard finite element stiffness matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
bim3a_osc_advection_diffusion


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 651
 -- Function File: [A] = bim3a_osc_advection_diffusion (MESH, ALPHA, V)

     Build the Scharfetter-Gummel stabilized OSC stiffness matrix for a
     diffusion-advection problem.

     For details on the Orthogonal Subdomain Collocation (OSC) method see:
     M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998.

     The equation taken into account is:

     - div (ALPHA ( grad (u) - grad (V) u)) = f

     where V is a piecewise linear continuous scalar functions and ALPHA is a
     piecewise constant scalar function.

     See also: bim3a_rhs, bim3a_osc_laplacian, bim3a_reaction, bim3a_laplacian,
     bim3c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the Scharfetter-Gummel stabilized OSC stiffness matrix for a
diffusion-...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
bim3a_osc_laplacian


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 507
 -- Function File: A = bim3a_osc_laplacian (MESH, EPSILON)

     Build the osc finite element stiffness matrix for a diffusion problem.

     For details on the Orthogonal Subdomain Collocation (OSC) method see:
     M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998.

     The equation taken into account is:

     - div (EPSILON grad (u)) = f

     where EPSILON is an element-wise constant scalar function.

     See also: bim3a_rhs, bim3a_reaction, bim2a_laplacian, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 70
Build the osc finite element stiffness matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
bim3a_reaction


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 406
 -- Function File: [C] = bim3a_reaction (MESH,DELTA,ZETA)

     Build the lumped finite element mass matrix for a diffusion problem.

     The equation taken into account is:

     DELTA * ZETA * u = f

     where DELTA is an element-wise constant scalar function, while ZETA is a
     piecewise linear conforming scalar function.

     See also: bim3a_rhs, bim3a_laplacian, bim2a_reaction, bim3a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 68
Build the lumped finite element mass matrix for a diffusion problem.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bim3a_rhs


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 414
 -- Function File: [B] = bim3a_rhs (MESH, F, G)

     Build the finite element right-hand side of a diffusion problem employing
     mass-lumping.

     The equation taken into account is:

     DELTA * u = F * G

     where F is an element-wise constant scalar function, while G is a piecewise
     linear conforming scalar function.

     See also: bim3a_reaction, bim3_laplacian, bim1a_reaction, bim2a_reaction.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Build the finite element right-hand side of a diffusion problem employing
mas...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 17
bim3c_global_flux


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 455
 -- Function File: [F] = bim3c_global_flux (MESH, U, ALPHA, V)

     Compute the flux associated with the Scharfetter-Gummel approximation of
     the scalar field U.

     The vector field is defined as:

     F =- ALPHA ( grad (u) - grad (V) u )

     where V is a piecewise linear continuous scalar functions and ALPHA is a
     piecewise constant scalar function.

     See also: bim3a_rhs, bim3a_reaction, bim3a_laplacian,
     bim3c_mesh_properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the flux associated with the Scharfetter-Gummel approximation of the
...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
bim3c_intrp


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
 -- Function File: DATA = bim3c_intrp (MSH, N_DATA, E_DATA, POINTS)

     Compute interpolated values of node centered multicomponent node centered
     field N_DATA and cell centered field N_DATA at an arbitrary set of points
     whos coordinates are given in the n_by_3 matrix POINTS.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute interpolated values of node centered multicomponent node centered fie...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
bim3c_mesh_properties


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
 -- Function File: [OMESH] = bim3c_mesh_properties(IMESH)

     Compute the properties of IMESH needed by BIM method and append them to
     OMESH as fields.

     See also: bim3a_reaction, bim3a_rhs, bim3a_laplacian.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the properties of IMESH needed by BIM method and append them to OMESH...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
bim3c_norm


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 768
 -- Function File: [NORM_U] = bim3c_norm(MESH,U,NORM_TYPE)

     Compute the NORM_TYPE-norm of function U on the domain described by the
     tetrahedral grid MESH.

     The input function U can be either a piecewise linear conforming scalar
     function or an elementwise constant scalar or vector function.

     The string parameter NORM_TYPE can be one among 'L2', 'H1' and 'inf'.

     Should the input function be piecewise constant, the H1 norm will not be
     computed and the function will return an error message.

     For the numerical integration of the L2 norm the second order quadrature
     rule by Keast is used (ref.  P. Keast, Moderate degree tetrahedral
     quadrature formulas, CMAME 55: 339-348 1986).

     See also: bim1c_norm, bim2c_norm.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the NORM_TYPE-norm of function U on the domain described by the
tetra...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
bim3c_pde_gradient


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
 -- Function File: [GX, GY, GZ] = bim3c_pde_gradient(MESH,U)

     Compute the gradient of the piecewise linear conforming scalar function U.

     See also: bim3c_global_flux.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 74
Compute the gradient of the piecewise linear conforming scalar function U.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
bim3c_tri_to_nodes


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 625
 -- Function File: U_NOD = bim3c_tri_to_nodes (MESH, U_TRI)
 -- Function File: U_NOD = bim3c_tri_to_nodes (M_TRI, U_TRI)
 -- Function File: [U_NOD, M_TRI] = bim3c_tri_to_nodes ( ... )

     Compute interpolated values at triangle nodes U_NOD given values at
     tetrahedral centers of mass U_TRI.  If called with more than one output,
     also return the interpolation matrix M_TRI such that ‘u_nod = m_tri *
     u_tri’.  If repeatedly performing interpolation on the same mesh the matrix
     M_TRI obtained by a previous call to ‘bim2c_tri_to_nodes’ may be passed as
     input to avoid unnecessary computations.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute interpolated values at triangle nodes U_NOD given values at tetrahedr...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
bim3c_unknowns_on_faces


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 251
 -- Function File: [NODELIST] = bim3c_unknowns_on_faces(MESH,FACELIST)

     Return the list of the mesh nodes that lie on the geometrical faces
     specified in FACELIST.

     See also: bim3c_unknown_on_faces, bim2c_pde_gradient, bim2c_global_flux.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Return the list of the mesh nodes that lie on the geometrical faces specified...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
bimu_bernoulli


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
 -- Function File: [BP, BN] = bimu_bernoulli (X)

     Compute the values of the Bernoulli function corresponding to X and - X
     arguments.

     See also: bimu_logm.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 80
Compute the values of the Bernoulli function corresponding to X and - X
argum...



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bimu_logm


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 143
 -- Function File: [T] = bimu_logm (T1,T2)

     Input:
        − T1:
        − T2:

     Output:
        − T:

     See also: bimu_bern.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
Input:
   − T1:
   − T2:

  





