Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Parallel ocean general circulation modeling
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Algorithm 719: Multiprecision translation and execution of FORTRAN programs
ACM Transactions on Mathematical Software (TOMS)
On properties of floating point arithmetics: numerical stability and the cost of accurate computations
Computational design of the NCAR community climate model
Parallel Computing - Special issue: climate and weather modeling
Design and performance of a scalable parallel community climate model
Parallel Computing - Special issue: climate and weather modeling
Iterative methods for solving linear systems
Iterative methods for solving linear systems
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Data organization and I/O in a parallel ocean circulation model
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
Pracniques: further remarks on reducing truncation errors
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Atmosperic Data Assimilation on Distributed-Memory Parallel Supercomputers
HPCN Europe 1998 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
GPU acceleration of cutoff pair potentials for molecular modeling applications
Proceedings of the 5th conference on Computing frontiers
Improving accuracy for matrix multiplications on GPUs
Scientific Programming
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Numerical reproducibility and stability of large scale scientific simulations, especially climate modeling, on distributed memory parallel computers are becoming critical issues. In particular, global summation of distributed arrays is most susceptible to rounding errors, and their propagation and accumulation cause uncertainty in final simulation results. We analyzed several accurate summation methods and found that two methods are particularly effective to improve (ensure) reproducibility and stability: Kahan's self-compensated summation and Bailey's double-double precision summation. We provide an MPI operator MPLSUMDD to work with MPI collective operations to ensure a scalable implementation on large number of processors. The final methods are particularly simple to adopt in practical codes.