Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions
Journal of Computational Physics
Expressing object-oriented concepts in Fortran 90
ACM SIGPLAN Fortran Forum
Object Oriented Programming Via FORTRAN 90/95
Object Oriented Programming Via FORTRAN 90/95
How to Express C++ Concepts in Fortran90
Scientific Programming
A grid-free abstraction of the Navier-Stokes equations in Fortran 95/2003
ACM Transactions on Mathematical Software (TOMS)
Formal constraints on memory management for composite overloaded operations
Scientific Programming
Design patterns for multiphysics modeling in Fortran 2003 and C++
ACM Transactions on Mathematical Software (TOMS)
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Abstract data types developed for computational science and engineering are frequently modeled after physical objects whose state variables must satisfy governing differential equations. Generalizing the associated algebraic and differential operators to operate on the abstract data types facilitates high-level program constructs that mimic standard mathematical notation. For non-trivial expressions, multiple object instantiations must occur to hold intermediate results during the expression's evaluation. When the dimension of each object's state space is not specified at compile-time, the programmer becomes responsible for dynamically allocating and de-allocating memory for each instantiation. With the advent of allocatable components in Fortran 2003 derived types, the potential exists for these intermediate results to occupy a substantial fraction of a program's footprint in memory. This issue becomes particularly acute at the highest levels of abstraction where coarse-grained data structures predominate. This paper proposes a set of rules for de-allocating memory that has been dynamically allocated for intermediate results in derived type calculus, while distinguishing that memory from more persistent objects. The new rules are applied to the design of a polymorphic time integrator for integrating evolution equations governing dynamical systems. Associated issues of efficiency and design robustness are discussed.