Results for “preconditioning techniques” — Page 3

DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sorbmatech{sup R}Cs, an Innovative Highly Selective Cs Sorbent for Wastewater Decontamination - 20065

The treatment of radioactive wastewater from the operating nuclear industry (energy production, reprocessing of spent fuel, decommissioning of shut-down facilities, etc.) or in case of incidental or accidental situation (such as Fukushima Daichii NPP accident) is an important issue requiring constant improvement of the technologies and techniques used to prevent radioactive releases into the environment and/or to reduce the production of secondary waste. CEA, Orano and CTI are collaborating since 2014, with the support of the French government's program 'investments for the future', to develop Sorbmatech{sup R}Cs, an innovative and patented selective sorbent (Grandjean and Barre 2014) to deal with the removal of radioactive {sup 137}Cs, one of the most hazardous isotope to be managed in nuclear waste, highly efficient either in agitated reactor or in column process. Sorbmatech{sup R}Cs sorbent consists of mesoporous silica particles loaded with potassium-copper hexacyanoferrate nanoparticles (KCu-HCF). This peculiar structure enables much faster sorption kinetics compared to denser crystalline structures, such as Silicotitanate or Zeolite sorbents, whose drawback consists in hindering the diffusion process through the material, and whose larger sorbent particles slow down the ion exchange process. The equilibrium of Sorbmatech{sup R}Cs is reached in few minutes, even at high flow rates in a fixed-bed column process (up to 10 m.h{sup -1} Darcy velocity) with low drop pressure. Moreover, Sorbmatech{sup R}Cs can be used over a wide pH range from 2 to 10 and has a very high selectivity towards {sup 137}Cs even in brine solution (saline, mineral or sea water). This new sorbent also has a K{sub d} higher than 10{sup 5} mL.g{sup -1} depending on the salinity of the wastewater, enabling a highly efficient removal of Cs trace in radioactive wastewater compared to Cs selective sorbent such as Zeolites and Silicotitanates. Its radiological resistance enables the treatment of high, medium and low activity wastewater. The CEA-Orano-CTI/ALSYS partnership leads to the development of a simple and low-cost synthetic route, which demonstrated large-scale manufacturing of the product on a batch of 100 kg. Two products have been developed and are ready for short run market introduction so far with grain size well adapted either for column processes or agitated reactors.. Finally, the industrial implementation has been studied and largely benefits from the properties of the sorbent. Indeed, its high sorption kinetics enable high flow rates resulting in a decrease of operation times, unit sizes, and volumes of secondary waste produced. Moreover, Sorbmatech{sup R}Cs is designed to be combined into a full and integrated solution, ranging from preliminary optimization of operating conditions through numerical dimensioning model, industrial implementation and treatment of the wastewater (through cartridge or preconditioned columns systems developed thanks to Orano's extensive expertise), to long-term stabilization of generated waste (under progress). (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗