Optimisation

Global Optimisation

It is possible to specify the following 2 optimisation flags for different operators:

• DO_GLOBAL_MAT_OP If TRUE (VALUE = 1), the globally assembled system matrix will be used to evaluate the operator. If FALSE (VALUE = 0), the operator will be evaluated elementally.
• DO_BLOCK_MAT_OP If TRUE (VALUE = 1), the elemental evaluation will be done using the elemental/local matrices (which are all concatenated in a block matrix, hence the name). If FALSE (VALUE = 0), the elemental evaluation will be done using the sum-factorisation technique.

The optimal configuration of these parameters depends on

• the computer environment (i.e. processor, BLAS library, ...)
• the discretisation (the mesh-size but mainly the POLYNOMIAL ORDER)

Choosing parameters

To set these parameters use the following rules of thumb:

• The global matrix approach is the most efficient option only for very low expansion order (P=1,P=2). Never set DO_GLOBAL_MAT_OP to true for an expansion order P>4 as it quickly becomes very expensive and you might run out of memory.
• The most efficient way of elementally evaluating an operator depends on the complexity of the operator in the sum-factorisation approach.
  1. For simple operators (such as BwdTrans and IProductWRTBase)
     • set DO_BLOCK_MAT_OP to TRUE for low orders (e.g. P<=4)
     • set DO_BLOCK_MAT_OP to FALSE in the other case
  2. For more complex operators (such as MassMatrixOp)
     • set DO_BLOCK_MAT_OP to TRUE for low and intermediate orders (e.g. P<=8)
     • set DO_BLOCK_MAT_OP to FALSE in the other case
  3. For very complex operators (such as HelmholtzMatrixOp) always set DO_BLOCK_MAT_OP to TRUE In general, the break-even point between the elemental matrix approach and the sum-factorisation technique is higher for triangular meshes than for quadrilateral meshes. That is why you for exmaple may want to set following flags for the IProductWRTBase operator: (quadrilateral mesh) set DO_BLOCK_MAT_OP to TRUE if P<=4 (triangular mesh) set DO_BLOCK_MAT_OP to TRUE if P<=6

Also note that, as opposed to the ELEMENTAL optimisation parameters, the GLOBAL parameters are problem dependent. In order to optimally set these parameters below, ideally, a 'self-tuning' optimisation suite which performs a series of test-runs based upon the mesh file above