model.bem()

Create a boundary element (BEM) model.

Syntax

model.bem().create(<tag>, "CoefficientPDE");

model.bem(<tag>).set(<prop>, <value>);

model.bem(<tag>).selection();

 

model.bem(<tag>).selection(); defines the selection for single-sided BEM boundaries. In addition, the following variants are available for double-sided boundaries:

•	Use model.bem(<tag>).selection("cont"); for a selection of double-sided boundaries where the field is continuous.

•	Use model.bem(<tag>).selection("discont"); for a selection of double-sided boundaries where the field is allowed to be discontinuous.

•	Use model.bem(<tag>).selection("edge"); for a selection of BEM edges in 3D.

For a complete list of methods available under selection(), see Selections.

The following general properties are available for model.bem:.

Table 2-7: General properties for BEM

property	value	default	description
background	Expression	0	Background field.
edgefluxname	String		Name of edge flux variable.
edgegradname	String[]		Names of edge gradient variables.
edgeradius	Expression		Radius of cylinders represented as edges.
fluxname	String		Name of boundary flux variable.
infval	Expression	0	Value at infinity (for Laplace equation).
normal	String[]		Boundary normals pointing out of BEM domain.
opname	String		Name of postprocessing operator.
varname	String		Name of field variable.
varnameback	String		Name of field variable on backside of double-sided boundaries.
varnamefront	String		Name of field variable on frontside of double-sided boundaries.

In addition, the following properties for the coefficient of the equation are available:.

Table 2-8: equation coefficient properties for BEM

property	value	default	description
a	String	0	Absorption coefficient.
al	String[]	{0,0,0}	Conservative flux convection coefficient.
be	String[]	{0,0,0}	Convection coefficient.
c	String	1	Diffusion coefficient.
cedge	String	1	Diffusion coefficient in cylinders represented as edges.
m	String	0	Condition at infinity for Helmholtz equation.

The following integration order properties are available:.

Table 2-9: Integration Order properties for BEM

property	value	default	description
intorderclose	String		Integration rule for close non-adjacent pairs of mesh elements.
intorderedge	String		Integration rule for pairs of mesh elements with a common edge (3D only).
intorderfar	String		Integration rule for distant pairs of mesh elements.
intordersame	String		Integration rule for pairs of mesh elements that coincide.
intordervertex	String		Integration rule for pairs of mesh elements with a common vertex.
intorderweak	String		Integration for weak equations.

The following symmetry properties are available:.

Table 2-10: Symmetry properties for BEM

property	value	default	description
sym1	off | scp | user	off	Use of symmetry plane orthogonal to x-axis.
sym1plane	Expression	0	Position of symmetry plane orthogonal to x-axis.
sym2	off | scp | user	off	Use of symmetry plane orthogonal to y-axis.
sym2plane	Expression	0	Position of symmetry plane orthogonal to y-axis.
sym3	off | scp | user	off	Use of symmetry plane orthogonal to z-axis.
sym3plane	Expression	0	Position of symmetry plane orthogonal to z-axis.

Finally, the following far-field approximation properties are available:.

Table 2-11: Far-Field Approximation properties for BEM

property	value	default	description
dampingparameter	Double	1	Damping parameter.
farfieldapprox	none | ACA | ACA+	none	Far-field approximation method.
farfieldboxsplitlimit	Integer	20	Number of mesh elements at which box splitting stops.
farfieldmindist	Double	0.5	Minimum relative distance of boxes using far-field approximation.
farfieldsvd	on | off	on	Use SVD compression in far-field approximation.
farfieldtol	Double	1e-3	Tolerance used in far-field approximation.
usedamping	on | off	off	Use damping parameter with iterative solver.

Example

The following example shows how to solve for a Helmholtz equation with outgoing waves at infinity in the exterior of a geometry. The example requires that the dependent variables u and bemflux already exist on the exterior boundaries.

Code for use with Java

model.intRule().create("ir1", "material1");

model.intRule("ir1").create("o1").order(4);

 

model.bem().create("bem1", "CoefficientPDE");

model.bem("bem1").selection().geom("geom1", 2).set(<list of exterior boundary numbers>);

model.bem("bem1").set("varname", "u");

model.bem("bem1").set("fluxname", "bemflux");

model.bem("bem1").set("normal", new String[]{"-nx", "-ny", "-nz"});

model.bem("bem1").set("a", "-1");

model.bem("bem1").set("m", "-1");

model.bem("bem1").set("opname", "bemop");

model.bem("bem1").set("intorderfar", "ir1");

model.bem("bem1").set("intorderclose", "ir1");

model.bem("bem1").set("intordersame", "ir1");

model.bem("bem1").set("intorderedge", "ir1");

model.bem("bem1").set("intordervertex", "ir1");

model.bem("bem1").set("intorderweak", "ir1");

Code for use with MATLAB

model.intRule().create('ir1', 'material1');

model.intRule('ir1').create('o1').order(4);

 

model.bem.create('bem1', 'CoefficientPDE');

model.bem('bem1').selection.geom('geom1', 2).set(<list of exterior boundary numbers>);

model.bem('bem1').set('varname', 'u');

model.bem('bem1').set('fluxname', 'bemflux');

model.bem('bem1').set('normal', {'-nx', '-ny', '-nz'});

model.bem('bem1').set('a', '-1');

model.bem('bem1').set('m', '-1');

model.bem('bem1').set('opname', 'bemop');

model.bem('bem1').set('intorderfar', 'ir1');

model.bem('bem1').set('intorderclose', 'ir1');

model.bem('bem1').set('intordersame', 'ir1');

model.bem('bem1').set('intorderedge', 'ir1');

model.bem('bem1').set('intordervertex', 'ir1');

model.bem('bem1').set('intorderweak", 'ir1');

See Also

model.coeff()