Automating FEA programming

In this paper we briefly describe a combined symbolic and numeric approach for solving mathematical models on parallel computers. An experimental software system, PIER, is being developed in Common Lisp to synthesize computationally intensive and domain formulation dependent phases of finite element analysis (FEA) solution methods. Quantities for domain formulation like shape functions, element stiffness matrices, etc., are automatically derived using symbolic mathematical computations. The problem specific information and derived formulae are then used to generate (parallel) numerical code for FEA solution steps. A constructive approach to specify a numerical program design is taken. The code generator compiles application oriented input specifications into (parallel) FORTRAN77 routines with the help of built-in knowledge of the particular problem, numerical solution methods and the target computer

Devito: Towards a generic Finite Difference DSL using Symbolic Python

Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide a powerful mechanism to speed up scientific Python computation that goes beyond traditional vectorization and pre-compilation approaches, while allowing domain scientists to build applications within the comforts of the Python software ecosystem. In this paper we present Devito, a new finite difference DSL that provides optimized stencil computation from high-level problem specifications based on symbolic Python expressions. We demonstrate Devito's symbolic API and performance advantages over traditional Python acceleration methods before highlighting its use in the scientific context of seismic inversion problems.Comment: pyHPC 2016 conference submissio

Computer algebra and transputers applied to the finite element method

Recent developments in computing technology have opened new prospects for computationally intensive numerical methods such as the finite element method. More complex and refined problems can be solved, for example increased number and order of the elements improving accuracy. The power of Computer Algebra systems and parallel processing techniques is expected to bring significant improvement in such methods. The main objective of this work has been to assess the use of these techniques in the finite element method. The generation of interpolation functions and element matrices has been investigated using Computer Algebra. Symbolic expressions were obtained automatically and efficiently converted into FORTRAN routines. Shape functions based on Lagrange polynomials and mapping functions for infinite elements were considered. One and two dimensional element matrices for bending problems based on Hermite polynomials were also derived. Parallel solvers for systems of linear equations have been developed since such systems often arise in numerical methods. Both symmetric and asymmetric solvers have been considered. The implementation was on Transputer-based machines. The speed-ups obtained are good. An analysis by finite element method of a free surface flow over a spillway has been carried out. Computer Algebra was used to derive the integrand of the element matrices and their numerical evaluation was done in parallel on a Transputer-based machine. A graphical interface was developed to enable the visualisation of the free surface and the influence of the parameters. The speed- ups obtained were good. Convergence of the iterative solution method used was good for gated spillways. Some problems experienced with the non-gated spillways have lead to a discussion and tests of the potential factors of instability

Automated derivation of the adjoint of high-level transient finite element programs

In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques. The approach relies on a high-level symbolic representation of the forward problem. In contrast to developing a model directly in Fortran or C++, high-level systems allow the developer to express the variational problems to be solved in near-mathematical notation. As such, these systems have a key advantage: since the mathematical structure of the problem is preserved, they are more amenable to automated analysis and manipulation. The framework introduced here is implemented in a freely available software package named dolfin-adjoint, based on the FEniCS Project. Our approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model, and employs the FEniCS finite element form compiler to automatically generate the low-level code for the derived models. The approach requires only trivial changes to a large class of forward models, including complicated time-dependent nonlinear models. The adjoint model automatically employs optimal checkpointing schemes to mitigate storage requirements for nonlinear models, without any user management or intervention. Furthermore, both the tangent linear and adjoint models naturally work in parallel, without any need to differentiate through calls to MPI or to parse OpenMP directives. The generality, applicability and efficiency of the approach are demonstrated with examples from a wide range of scientific applications

Nmag micromagnetic simulation tool - software engineering lessons learned

We review design and development decisions and their impact for the open source code Nmag from a software engineering in computational science point of view. We summarise lessons learned and recommendations for future computational science projects. Key lessons include that encapsulating the simulation functionality in a library of a general purpose language, here Python, provides great flexibility in using the software. The choice of Python for the top-level user interface was very well received by users from the science and engineering community. The from-source installation in which required external libraries and dependencies are compiled from a tarball was remarkably robust. In places, the code is a lot more ambitious than necessary, which introduces unnecessary complexity and reduces main- tainability. Tests distributed with the package are useful, although more unit tests and continuous integration would have been desirable. The detailed documentation, together with a tutorial for the usage of the system, was perceived as one of its main strengths by the community.Comment: 7 pages, 5 figures, Software Engineering for Science, ICSE201

ATMOL: A Domain-Specific Language for Atmospheric Modeling

This paper describes the design and implementation of ATMOL: a domain-specific language for the formulation and implementation of atmospheric models. ATMOL was developed in close collaboration with meteorologists at the Royal Netherlands Meteorological Institute (KNMI) to ensure ease of use, concise notation, and the adoptation of common notational conventions. ATMOL’s expressiveness allows the formulation of high-level and low-level model details as language constructs for problem refinement and code synthesis. The atmospheric models specified in ATMOL are translated into efficient numerical codes with CTADEL, a tool for symbolic manipulation and code synthesis

ATMOL: A Domain-Specific Language for Atmospheric Modeling

This paper describes the design and implementation of ATMOL: a domain-specific language for the formulation and implementation of atmospheric models. ATMOL was developed in close collaboration with meteorologists at the Royal Netherlands Meteorological Institute (KNMI) to ensure ease of use, concise notation, and the adoptation of common notational conventions. ATMOL’s expressiveness allows the formulation of high-level and low-level model details as language constructs for problem refinement and code synthesis. The atmospheric models specified in ATMOL are translated into efficient numerical codes with CTADEL, a tool for symbolic manipulation and code synthesis

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques