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Bempp::AcaOptions Struct Reference
Weak-form assembly

Adaptive cross approximation (ACA) parameters. More...

#include </home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/aca_options.hpp>

Public Types

enum  AcaAssemblyMode {
  MIN_ASSEMBLY_MODE, GLOBAL_ASSEMBLY = MIN_ASSEMBLY_MODE, LOCAL_ASSEMBLY, HYBRID_ASSEMBLY,
  MAX_ASSEMBLY_MODE = HYBRID_ASSEMBLY
}
 ACA assembly mode. See documentation of the member mode for more information.
 
enum  ReactionToUnsupportedMode {
  MIN_REACTION, IGNORE = MIN_REACTION, WARNING, ERROR,
  MAX_REACTION = ERROR
}
 Actions to take when an unsupported assembly mode is detected. More...
 

Public Member Functions

 AcaOptions ()
 Initialize ACA parameters to default values.
 

Public Attributes

double eps
 Estimate of the desired approximation accuracy. More...
 
double eta
 Cluster-pair admissibility parameter. More...
 
unsigned int minimumBlockSize
 Minimum size of blocks approximated with ACA. More...
 
unsigned int maximumBlockSize
 Maximum allowed block size. More...
 
unsigned int maximumRank
 Maximum rank of blocks stored in the low-rank format. More...
 
AcaAssemblyMode mode
 ACA assembly mode. More...
 
ReactionToUnsupportedMode reactionToUnsupportedMode
 Action to take when an unsupported assembly mode is detected. More...
 
bool recompress
 Recompress ACA matrix after construction? More...
 
bool outputPostscript
 If true, hierarchical matrix structure will be written in PostScript format at the end of the assembly procedure. More...
 
std::string outputFname
 Name of the output PostScript file. More...
 
double scaling
 Estimate of the magnitude of typical entries of the matrix to be approximated. More...
 
bool useAhmedAca
 Choice of ACA variant. More...
 
int firstClusterIndex
 Index of the first block cluster to be approximated using ACA. More...
 
bool globalAssemblyBeforeCompression
 Do global assembly before ACA? More...
 

Detailed Description

Adaptive cross approximation (ACA) parameters.

Member Enumeration Documentation

enum Bempp::AcaOptions::ReactionToUnsupportedMode

Actions to take when an unsupported assembly mode is detected.

See Also
reactionToUnsupportedMode.

Member Data Documentation

double Bempp::AcaOptions::eps

Estimate of the desired approximation accuracy.

Default value: 1e-4.

double Bempp::AcaOptions::eta

Cluster-pair admissibility parameter.

Default value: 1.2.

int Bempp::AcaOptions::firstClusterIndex

Index of the first block cluster to be approximated using ACA.

This parameter is included to facilitate debugging of ACA algorithms. If it is set to a nonnegative value, ACA will process block cluster with index firstClusterIndex first.

Default value: -1 (meaning that this parameter is ignored).

bool Bempp::AcaOptions::globalAssemblyBeforeCompression

Do global assembly before ACA?

Deprecated:
This parameter is deprecated and should not be used in new code. If set to true (default), it is ignored. Otherwise it is equivalent to setting the mode parameter to LOCAL_ASSEMBLY.

Referenced by Bempp::AssemblyOptions::switchToAcaMode().

unsigned int Bempp::AcaOptions::maximumBlockSize

Maximum allowed block size.

Matrix blocks with side larger than this value will be split. This can be used to limit the time devoted to (serial) processing of an individual block, especially when a large number of threads is used.

Default value: UINT_MAX.

unsigned int Bempp::AcaOptions::maximumRank

Maximum rank of blocks stored in the low-rank format.

Blocks judged to have higher rank will be stored in the dense format.

Default value: UINT_MAX.

unsigned int Bempp::AcaOptions::minimumBlockSize

Minimum size of blocks approximated with ACA.

Matrix blocks whose smaller side is less than this value will be stored in the dense format (ACA will not be attempted on these blocks).

Default value: 16.

AcaAssemblyMode Bempp::AcaOptions::mode

ACA assembly mode.

This parameter lets you choose between three ways of discretizing operators using ACA. Suppose you have an integral operator $\mathcal A$ that you want to discretize using a test space $U$ and and trial space $V$.

  1. If mode is set to GLOBAL_ASSEMBLY (default), ACA is used in the most straightforward way possible, i.e. to approximate blocks of the operator $\mathcal A$ discretized with the basis functions of $U$ and $V$.

  2. If mode is set to LOCAL_ASSEMBLY, the discretization $A$ of $\mathcal A$ is constructed as a sum

    \[ A = \sum_{i=1}^n \alpha_i P_i A_i Q_i, \]

    where $n$ is a small integer, $\alpha_i$ scalar coefficients, $P_i$ and $Q_i$ sparse matrices and $A_i$ H-matrices representing integral operators discretized with basis functions whose support extends over single elements only (for example functions linear on a single element and zero everywhere else). In most practical cases all matrices $A_i$ are equal (and obviously only a single copy is stored in memory). This assembly mode takes advantage of the fact that ACA becomes more efficient as the support of test and trial functions is reduced. Thus, assembly in LOCAL_ASSEMBLY mode is often much faster than in GLOBAL_ASSEMBLY mode. However, this comes at the price of increased memory use, since the matrices $A_i$ are typically much bigger than $A$. In addition, the DiscreteBoundaryOperator::asDiscreteAcaBoundaryOperator() function is not currently implemented for products of operators, so discrete operators created in the LOCAL_ASSEMBLY modes cannot be converted into single H-matrices. Thus, they cannot be used for H-LU preconditioning.

    More information about the matrices $P_i$ and $Q_i$ can be found in the documentation of the SyntheticIntegralOperator class. See also the documentation of non-member constructors of particular integral operators, such as laplace3dSingleLayerBoundaryOperator() and helmholtz3dHypersingularBoundaryOperator(), for explicit expressions used to represent these operators in the LOCAL_ASSEMBLY mode.

  3. The HYBRID_ASSEMBLY mode is available for operators whose weak form can be written as

    \[ \int_\Gamma \int_\Sigma f(x) \, K(x, y) \, g(y) \, \mathrm{d}\Gamma(x) \,\mathrm{d}\Sigma(y), \]

    where $f(x)$ and $g(y)$ are scalar basis functions of $U$ and $V$ (not any transformations of them, i.e. not their surface curls, divs etc.), *at least as long as the supports of $f(x)$ and $g(y)$ do not overlap*. (Note that this is possible—for $x \neq y$—even for hypersingular operators.) In this mode, individual blocks of the operator are assembled differently, depending on whether the bounding box of the supports of the test basis functions contributing to a given block overlaps or not with the bounding box of the supports of the trial basis functions.

    Blocks for which these two boxes overlap are assembled as in the GLOBAL_ASSEMBLY mode, using an arbitrary weak form (possibly one that does not have the form defined above). For the remaining blocks, ACA is used to approximate the discretization of the weak form as defined above with test and trial functions taken as the restrictions of the the basis functions of $U$ and $V$ to single elements. After the assembly of each such block, linear combinations of its rows and columns are used to build a low-rank representation of the block in the original bases of $U$ and $V$.

    This mode combines the advantages of LOCAL_ASSEMBLY (fast matrix construction) and GLOBAL_ASSEMBLY (low memory consumption, representation in the form of a single H-matrix). However, at present it cannot be used for Maxwell operators, which require vector basis functions.

Some integral operators may not support the LOCAL_ASSEMBLY and HYBRID_ASSEMBLY modes. How these operators behave when one of these modes is chosen can be controlled with the reactionToUnsupportedMode parameter.

Referenced by Bempp::SyntheticIntegralOperator< BasisFunctionType_, ResultType_ >::getContextsForInternalAndAuxiliaryOperators(), Bempp::laplace3dAdjointDoubleLayerBoundaryOperator(), Bempp::laplace3dDoubleLayerBoundaryOperator(), Bempp::laplace3dHypersingularBoundaryOperator(), Bempp::laplace3dSingleLayerBoundaryOperator(), Bempp::maxwell3dSingleLayerBoundaryOperator(), Bempp::modifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(), Bempp::modifiedHelmholtz3dDoubleLayerBoundaryOperator(), Bempp::modifiedHelmholtz3dHypersingularBoundaryOperator(), Bempp::modifiedHelmholtz3dSingleLayerBoundaryOperator(), and Bempp::AssemblyOptions::switchToAcaMode().

std::string Bempp::AcaOptions::outputFname

Name of the output PostScript file.

See Also
outputPostscript.

Default value: "aca.ps".

bool Bempp::AcaOptions::outputPostscript

If true, hierarchical matrix structure will be written in PostScript format at the end of the assembly procedure.

Default value: false.

ReactionToUnsupportedMode Bempp::AcaOptions::reactionToUnsupportedMode

Action to take when an unsupported assembly mode is detected.

This parameter controls what happens if an integral operator is requested to construct its discrete weak form in an ACA mode (LOCAL_ASSEMBLY or HYBRID_ASSEMBLY) it does not support.

If reactionToUnsupportedMode is set to IGNORE, the operator silently assembles its discrete weak form in the GLOBAL_ASSEMBLY mode.

It reactionToUnsupportedMode is set to WARNING (default), the operator emits a warning message to the standard output and assembles its discrete weak form in the GLOBAL_ASSEMBLY mode.

If reactionToUnsupportedMode is set to ERROR, the operator throws an exception.

Referenced by Bempp::AssemblyOptions::switchToAcaMode().

bool Bempp::AcaOptions::recompress

Recompress ACA matrix after construction?

If true, blocks of H matrices are agglomerated in an attempt to reduce memory consumption.

Warning: this procedure is not parallelised yet, therefore it may be slow.

Default value: false.

double Bempp::AcaOptions::scaling

Estimate of the magnitude of typical entries of the matrix to be approximated.

Usually does not need to be changed. Default value: 1.

Referenced by Bempp::WeakFormAcaAssemblyHelper< BasisFunctionType, ResultType >::scale().

bool Bempp::AcaOptions::useAhmedAca

Choice of ACA variant.

If true, the default implementation of the ACA algorithm from the AHMED library will be used.

If false, an alternative formulation of ACA will be used. This formulation appears to be more successful in the approximation of operators whose matrices contain empty blocks (like the double-layer boundary operator for the Laplace equation) and in general it tries harder to find a low-rank approximation of a block before falling back to a dense representation.

Default value: false.

The documentation for this struct was generated from the following files:
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