A note on domain decomposition approaches for solving 3D variational data assimilation models

D’Amore, Luisa; Cacciapuoti, Rosalba

doi:10.1007/s11587-019-00432-4

Cited by 5 publications

(5 citation statements)

References 26 publications

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“…The present work is placed in the context of a research activity devoted to the development of scalable algorithms for using data assimilation in large‐scale applications 15‐18 . Main purpose of this article is to address a mathematical framework for using a DD‐based approach for KF method that is both relatively easy to implement and computationally efficient.…”

Section: Discussionmentioning

confidence: 99%

“…The present work is placed in the context of a research activity devoted to the development of scalable algorithms for using data assimilation in large-scale applications. [15][16][17][18] Main purpose of this article is to address a mathematical framework for using a DD-based approach for KF method that is both relatively easy to implement and computationally efficient. The key point of the present work is to prove the necessary results that underpin this framework by considering, let us say, a first-level decomposition.…”

Section: Discussionmentioning

confidence: 99%

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A scalable Kalman filter algorithm: Trustworthy analysis on constrained least square model

D’Amore

Cacciapuoti

Mele

2020

Concurrency and Computation

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Summary Kalman filter (KF) is one of the most important and common estimation algorithms. We introduce an innovative designing of Kalman filter algorithm based on domain decomposition (we call it DD‐KF). DD‐KF involves decomposition of the whole computational problem, partitioning of the solution and a slight modification of KF algorithm allowing a correction at run‐time of local solutions. The resulted parallel algorithm consists of concurrent copies of KF algorithm, each one requiring the same amount of computations on each subdomain and an exchange of boundary conditions between adjacent subdomains. Main advantage of this approach is that it can be potentially applied in a moderately nonintrusive manner to existing codes for tracking and controlling systems in location, navigation, in computer graphics and in much more state estimation problems. To highlight the capability of DD‐KF of exploiting the computing power provided by future designs of microprocessors based on multi/many‐cores CPU/GPU technologies, we consider DD both at physical core level and at microprocessor level and we discuss scalability of DD‐KF algorithm at coarse and fine grained level. Throughout the present work, we derive and discuss DD‐KF algorithm for solving constrained least square model, which underlies any data sampling and estimation problem.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A scalable Kalman filter algorithm: Trustworthy analysis on constrained least square model

D’Amore

Cacciapuoti

Mele

2020

Concurrency and Computation

Self Cite

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“…where I i is defined in (21) and J| I i ,I j is defined in (20), O 1,2 is the overlapping operator and µ > 0 is the regularization parameter.…”

Section: Definitionmentioning

confidence: 99%

“…The primary motivation of Schwarz based DD methods was the inherent parallelism arising from a flexible, adaptive and independent decomposition of the given problem into several subproblems, though they can also reduce the complexity of sequential solvers. Schwarz Methods and theoretical frameworks are, to date, the most mature for this class of problems 20,26,38 . MOR techniques are based on projection of the full order model onto a lower dimensional space spanned by a reduced order basis.…”

Section: Introductionmentioning

confidence: 99%

Parallel framework for Dynamic Domain Decomposition of Data Assimilation problems a case study on Kalman Filter algorithm

Cacciapuoti,

D'Amore

2022

Preprint

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We focus on PDE-based Data Assimilation problems (DA) solved by means of variational approaches and Kalman Filter algorithm. Recently, we presented a Domain Decomposition framework (we call it DD-DA, for short) performing a decomposition of the whole physical domain along space and time directions, and joining the idea of Schwarz's methods and Parallel in Time (PinT)-based approaches. For effective parallelization of domain decomposition algorithms, the computational load assigned to sub domains must be equally distributed. Usually computational cost is proportional to the amount of data entities assigned to partitions. Good quality partitioning also requires the volume of communication during calculation to be kept at its minimum. In order to deal with DD-DA problems where the observations are non uniformly distributed and general sparse, in the present work we employ a parallel load balancing algorithm -based on adaptive and dynamic defining of boundaries of DD -which is aimed to balance workload according to data location.We call it DyDD. As the numerical model underlying DA problems arising from the socalled discretize-then-optimize approach is the Constrained Least Square model (CLS), we will use CLS as a reference state estimation problem and we validate DyDD on different scenarios.

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“…Schwarz methods and theoretical frameworks are, to date, the most mature for this class of problems. 13,16,17,18 MOR techniques are based on projection of the full-order model onto a lower dimensional space spanned by a reduced-order basis. These methods has been used extensively in a variety of fields for efficient simulations of highly intensive computational problems.…”

Section: Introductionmentioning

confidence: 99%

Parallel framework for dynamic domain decomposition of data assimilation problems: a case study on Kalman Filter algorithm

D’Amore

Cacciapuoti

2021

Comp and Math Methods

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We focus on Partial Differential Equation (PDE)-based Data Assimilation problems (DA) solved by means of variational approaches and Kalman filter algorithm. Recently, we presented a Domain Decomposition framework (we call it DD-DA, for short) performing a decomposition of the whole physical domain along space and time directions, and joining the idea of Schwarz's methods and parallel in time approaches. For effective parallelization of DD-DA algorithms, the computational load assigned to subdomains must be equally distributed. Usually computational cost is proportional to the amount of data entities assigned to partitions. Good quality partitioning also requires the volume of communication during calculation to be kept at its minimum. In order to deal with DD-DA problems where the observations are nonuniformly distributed and general sparse, in the present work we employ a parallel load balancing algorithm based on adaptive and dynamic defining of boundaries of DD-which is aimed to balance workload according to data location. We call it DyDD. As the numerical model underlying DA problems arising from the so-called discretize-then-optimize approach is the constrained least square model (CLS), we will use CLS as a reference state estimation problem and we validate DyDD on different scenarios.

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A note on domain decomposition approaches for solving 3D variational data assimilation models

Cited by 5 publications

References 26 publications

A scalable Kalman filter algorithm: Trustworthy analysis on constrained least square model

A scalable Kalman filter algorithm: Trustworthy analysis on constrained least square model

Parallel framework for Dynamic Domain Decomposition of Data Assimilation problems a case study on Kalman Filter algorithm

Parallel framework for dynamic domain decomposition of data assimilation problems: a case study on Kalman Filter algorithm

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