The Mathematica package AceGen is used for the automatic
derivation of formulae needed in numerical procedures. Symbolic derivation of
the characteristic quantities (e.g. gradients, tangent operators, sensitivity vectors,…) leads to exponential behavior of derived
expressions, both in time and space. A new approach, implemented in AceGen,
avoids this problem by combining several techniques: symbolic and algebraic
capabilities of Mathematica, automatic differentiation technique, automatic
code generation, simultaneous optimization of expressions and theorem proving
by a stochastic evaluation of the expressions. The multi-language capabilities
of AceGen can be used for a rapid prototyping of numerical procedures in script
languages of general problem solving environments like Mathematica or Matlab©
as well as to generate highly optimized and efficient compiled language codes
in FORTRAN or C. Through a unique user interface the derived formulae can be
explored and analyzed.
The AceGen package also provides a collection of prearranged
modules for the automatic creation of the interface between the automatically
generated code and the numerical environment where the code would be executed.
The AceGen package directly supports several numerical environments such as:
MathLink connection to Mathematica, AceFEM is a research finite element
environment based on Mathematica, FEAP© is a research finite element
environment written in FORTRAN, ELFEN© and ABAQUS© are
the commercial finite element environments written in FORTRAN etc.. The multi-language and multi-environment capabilities
of AceGen package enable generation of numerical codes for various numerical
environments from the same symbolic description. The use of AceGen offers a
general approach to symbolic description of direct and sensitivity analysis of
the most important formulations that appear in description of problems by
finite element method (steady state, transient, coupled and coupled transient
problems). The AceGen package rejects the traditional assumption that
transition from symbolic codes to type-compiled codes is impracticable and that
the symbolically generated codes are intrinsically too slow for large-scale
found in the product
extends the use of Mathematica to problems where direct use of Mathematica
leads to expression swell (e.g. nonlinear finite elements, gradients of
complicated functions needed within optimization procedures, etc.). It
rejects the traditional assumption that transition from symbolic codes to
type-compiled codes is impracticable and that the symbolically generated
codes are intrinsically too slow for large-scale numerical computations.
- A new
approach, implemented in AceGen, avoids the expression swell problem by
combining several techniques: symbolic and algebraic capabilities of
Mathematica, automatic differentiation technique, automatic code
generation, simultaneous optimization of expressions and theorem proving
by a stochastic evaluation of the expressions.
of expressions and generation of control structures (Do, If) is performed
over multiple notebook cells. The appropriate intermediate variables are
is appropriate for large problems where also intermediate expressions can
be subjected to the uncontrolled swell.
includes the forward and backward mode of automatic differentiation
technique with several unique enhancements with respect to the standard
automatic differentiation (AD) technique.
procedure can be initiated at any time and at any point of derivation of
the formulae and as many times as required.
standard implementation of automatic differentiation as code-to-code
translation is replaced by the method that consistently extends the
current code rather than produces a new one.
the reason of efficiency, the results of all previous uses of AD are
accounted for when AD is used several times inside the same subroutine.
offers differentiation with respect to indexed variables.
Multi - language
and multi - environment code generation
offers multi-language code generation (Fortran/Fortran90, C, Mathematica
language, Matlab language) and automatic interface to general numerical
environments (MathLink connection to Mathematica, Matlab) and specialized
finite element environments (AceFEM, FEAP, ELFEN, ABAQUS, …)
and multi-environment capability enables that once the problem is
formulated in AceGen it can be directly exported to various commercial
numerical environments. Practice shows that at the research stage of the
derivation of a new numerical software, different languages and different
platforms are the best means for the assessment of specific performances
and, of course, failures of the numerical model. Using the classical
approach, re-coding of the element in different languages would be
extremely time consuming and is never done. With the AceGen concepts
re-coding comes practically for free, since the code is automatically
generated for several languages and for several platforms from the same
basic symbolic description.
Code efficiency and
- One of
the advantages of the AceGen approach is also that the symbolic
description of the numerical procedure is complete in a sense that almost
no external pre-arranged subroutines are called from the generated code.
No other data are accessed apart form those provided through the list of
parameters of the user subroutine. Code, generated on these principles, is
a bit longer than it would be if the reusable parts of the code were used.
However, there are advantages of this approach in numerical efficiency,
portability of the generated code to different operational systems and to
different numerical environments and easy parallelization.
many industrial sectors numerical simulations have become part of everyday
practice. The development of new numerical models has therefore become an
inseparable part of specific industrial projects and is no longer a
long-term research task as it was the case previously. The use of AceGen
offers on-demand generation of numerical procedures.
References or list
of publications related to the product
Jože, WRIGGERS, Peter. Automation of finite element methods. Switzerland:
Springer, 2016. XXVI.
http://link.springer.com/book/10.1007%2F978-3-319-39005-5, doi: 10.1007/978-3-319-39005-5. http://www.springer.com/-/1/AVXo2wyFKEAfyFF0Zyqj
Blaž, KORELC, Jože. Closed-form representation of matrix functions in the
formulation of nonlinear material models. Finite Elements in Analysis and
Design, 2016, 111:19-32
Jože. Automation of primal and sensitivity analysis of transient coupled
problems. Comput. mech., 2009,
J., (2002), Multi-language and Multi-environment Generation of Nonlinear
Finite Element Codes,
Engineering with Computers, 2002, vol. 18, n. 4,str. 312-327
J. (1997), Automatic generation of finite-element code by simultaneous
optimization of expressions, Theoretical Computer Science, 187, 231-248.
J. (1996), Symbolic Approach in Computational Mechanics and its
Application to the Enhanced Strain Method, Doctoral Dissertation, Institut of Mechanics, TH Darmstadt, Germany.