Exploiting Repeated Structures and Vectorization in Modelica

Abstract

Large and highly-detailed Modelica models are frequently modeled by utilizing repeated structures, which is a repetition of various elements that are linked together in an iterative manner. While the Modelica language standard supports the representation of repeated structures, most Modelica compilers do not exploit their advantages for efficient simulations. Instead, all repeated equations are flattened and all array variables are expanded. This leads to unnecessarily long compile times and higher memory consumption. Another aspect that has been yet inadequately considered and is closely connected to repeated structures is vectorization. The vector units of modern CPUs can be engaged to perform SIMD (Single Instruction, Multiple Data) operations, executing the same instruction on multiple data points in parallel. This reveals a high potential for faster simulations. This paper discusses the advantages of utilizing repeated structures for modeling in order to achieve both faster compilation and simulation times. The potentials of preserving for loops throughout compilation are demonstrated using a basic implementation in the OpenModelica Compiler. The effect on the simulation time by enabling vectorization is demonstrated for an appropriate model.

A New OpenModelica Compiler High Performance Frontend

“…The new frontend offers the feature to convert arrays of component models to array equations and to keep arrays during flattening. Additionally, the current backend has been extended prototypically, by exploiting previous work by (Schuchart et al, 2015) to treat for-equations during model translation and by (Franke et al, 2015) to treat unexpanded arrays and array slices in the generated code.…”

Towards a High-Performance Modelica Compiler

“…However, the structural analysis of the system equations, and the consequent code generation, is still carried out on a fully flattened and expanded system. Some work has been carried out in the past on methods to carry out the structural analysis of the system while keeping repetitive structures such as arrays of variables and loop equations as atomic entities, see (Arzt et al, 2014), possibly also considering issues such as CPU cache misses in the generated code, see (Schuchart et al, 2015). (Zimmer, 2009) proposed methods to exploit the objectoriented structure of large system models, rather than going through full flattening of the equations, in order to come up with more efficient code generation strategies.…”

Transformation of Differential Algebraic Array Equations to Index One Form

“…This has significant drawbacks for large array equations. In (Schuchart, et al, 2015) it is shown how special forloops can be handled so that they need not to be expanded for the Pantelides algorithm and are retained in the generated code.…”