Bentonite-based engineered barriers are a key component of many repository designs for the confinement of high-level radioactive waste and spent fuel. Given the complexity and interaction of the phenomena affecting the barrier, coupled hydro-mechanical (HM) and thermo-hydro-mechanical (THM) numerical analyses are a potentially useful tool for a better understanding of their behaviour. In this context, a Task (INBEB) was undertaken to study, using numerical analyses, the hydro-mechanical and thermo-hydro-mechanical Interactions in Bentonite Engineered Barriers within the international cooperative project DECOVALEX 2019. Two large scale tests, largely complementary, were selected for modelling: EB and FEBEX. The EB experiment was carried out under isothermal conditions and artificial hydration and it was dismantled after 10.7 years. The FEBEX test was a temperature-controlled non-isothermal test combined with natural hydration that underwent two dismantling operations, a partial one after 5 years of heating and a final one after a total of 18.4 years of heating. Direct observation of the state of the barriers was possible during the dismantling operations so that the evolution of barrier heterogeneity under transient conditions could be determined. Four teams performed the HM and THM numerical analyses using a variety of computer codes, formulations and constitutive laws. For each experiment, the basic features of the analyses are described and the comparison between calculations and field observations are presented and discussed. Comparisons involve measurements performed during the performance of the test and data gathered during dismantling. A final evaluation of the performance of the modelling closes the paper.

The paper is devoted to the formulation of a mathematical model which enables analysis of coupled thermo-hydro-mechanical (THM) processes with a special focus on processes in bentonite and bentonite-based sealing barriers which are component of designs of deep geological repositories for a high-level radioactive waste including the spent nuclear fuel. Such modelling is important as the analysis of coupled THM processes in the near field is crucial for the understanding of the long-term behaviour of the barriers. The developed model uses generally available data from standard tests but attempts to incorporate special characteristics of the bentonite behaviour, let us mention the oversaturation, swelling and strong couplings of the processes. The model is implemented via COMSOL Multiphysics and validated by the simulation of THM processes which were monitored during operation of the FEBEX experiment and analysed during two dismantling phases of the experiment.

The paper deals with boundary optimal control methods for partial differential equation (PDE) problems with both target and control variables on specified parts of the boundary of the problem domain. Besides the standard aim in approximation of the target variable the paper also addresses an inverse identification of conditions on an inaccessible part of the boundary by letting them play the role of a control variable function and by overimposing boundary conditions at another part of the boundary of the given domain. The paper shows the mathematical formulation of the problem, the arising (regularized) Karush–Kuhn–Tucker (KKT) system and introduces preconditioners for the solution of the regularized system. The spectral analysis of the preconditioner, analysis of the approximation of the target function and boundary condition on an inaccessible part of the boundary and numerical tests with the proposed preconditioning techniques are included.

Optimal control methods are applied in various problems and can be efficient also for solving inverse problems, such as parameter identification and boundary control which arise in many important applications. For boundary optimal control methods one can identify conditions on an inaccessible part of the boundary by letting them play the role of a control variable function and by overimposing boundary conditions at another part of the boundary of the given domain. The paper shows a mathematical formulation of the problem, the arising (regularized) Karush-Kuhn-Tucker (KKT) system and introduces a preconditioner for this system. The spectral analysis of the preconditioner and numerical tests with preconditioning are included. 1 Parameter identification problems An important type of optimal control problems are problems where one must identify some unknown boundary conditions on a part of the boundary, for instance where a part of some equipment is not accessible for measurements. Another important class of problems arise if one needs to identify some material dependent coefficients in a differential equation. For various types of corresponding inverse problems, see [9]. To identify the unknown boundary conditions, one can overimpose boundary values at an accessible part of the domain and introduce a control variable to represent the missing boundary data. For an example of such a problem in connection with heat flow, see [10, 11, 8, 9]. For some earlier uses of optimal control methods for differential equation constraints and related preconditioners, see [3, 2]. The arising first order necessary optimality condition can be reduced to a two-by-two block operator system of equations, the discretized form of which is solved by an iterative method. Thereby a very efficient preconditioning method is used, each application of which involves the solution of two systems consisting of the discretized second order differential equation operator added to a

The DECOVALEX Project is an on-going international research collaboration, established in 1992, to advance the understanding and modeling of coupled Thermal (T), Hydrological (H), Mechanical (M) and Chemical (C) processes in geological in geological systems. This document is the final report of Task D which was proposed by the DECOVALEX Project and coordinated by CIMNE_UPC, presenting the technical definitions of the problems studied, approaches applied, achievements made and outstanding issues for future research. Task D of the DECOVALEX 2019 project is devoted to the study of the hydro-mechanical (HM) and thermo-hydro-mechanical (THM) Interactions in Bentonite Engineered Barriers (INBEB). Special attention is paid to the evolution of barrier heterogeneity under transient conditions. A proper understanding of the processes occurring during the transient period requires the appropriate simulation of the behavior of the engineered barrier by means of coupled numerical analyses. In this context, the main objective of the Task is to assess the capabilities of numerical formulations and codes to simulate and interpret the HM and THM behavior of the bentonite barrier, with a particular focus on the final state reached on saturation.

The paper is motivated by a strong interest in numerical analysis of flow in fractured porous media, e.g., rocks in geo-engineering applications. It follows the conception of porous media as a continuum with fractures which are represented as lower dimensional objects. In the paper, the finite element discretization of the flow in coupled continuum and fractures is used; fluid pressures serve as the basic unknowns. In many applications, the flow is connected with deformations of the porous matrix; therefore, the hydro-mechanical coupling is also considered. The fluid pressure is transferred to the mechanical load in both pores and fractures and the considered mechanical model involves elastic deformations of the porous matrix and opening/closing of the fractures with the non-penetration constraint. The mechanical model with this constraint is implemented via the technique of the Lagrange multipliers, duality formulation, and combination with a suitable domain decomposition method. There is usually lack of information about problem parameters and they undergo many uncertainties coming e.g. from the heterogeneity of rock formations and complicated realization of experiments for parameter identification. These experiments rarely provide some of the asked parameters directly but require solving inverse problems. The stochastic (Bayesian) inversion is natural due to the mentioned uncertainties. In this paper, the implementation of the Bayesian inversion is realized via Metropolis-Hastings Markov chain Monte Carlo approach. For the reduction of computational demands, the sampling procedure uses the delayed acceptance of samples based on a surrogate model which is constructed during a preliminary sampling process. The developed hydro-mechanical model and the implemented Bayesian inversion are tested on two types of model inverse problems.

The DECOVALEX Project is an on-going international research collaboration, established in 1992, to advance the understanding and modeling of coupled Thermal (T), Hydrological (H), Mechanical (M) and Chemical (C) processes in geological in geological systems. This document is the final report of Task G which was proposed by the Swedish Radiation Safety Authority (SSM) and coordinated by geomecon GmbH, presenting the technical definitions of the problems studied, approaches applied, achievements made and outstanding issues for future research. Task G in DECOVALEX-2019 is primarily concerned with the evolution of transmissivity throughout the lifetime of a repository for radioactive waste, and in particular of spent nuclear fuel, in sparsely fractured and competent crystalline rock masses, and the representation of these processes via numerical simulation. The numerical simulations were to be evaluated for their suitability, and to be validated. Over the course of the work presented here, not only were transmissivity changes and the best approaches to simulate those change examined, but also strategies were to be developed on how to monitor transmissivity change. Guidelines on what a control program and a monitoring system for a repository should include and be able to measure, and how this can be done in practice, was a key objective of the research project.

The paper deals with the identification of material parameters characterizing components in heterogeneous geocomposites provided that the interfaces separating different materials are known. We use the optimal control approach with flux type cost functionals. Since solutions to the respective state problems are not regular, in general, the original cost functionals are expressed in terms of integrals over the computational domain using the Green formula. We prove the existence of solutions to the optimal control problem and establish convergence results for appropriately defined discretizations. The rest of the paper is devoted to computational aspects, in particular how to handle high sensitivity of the problem on the accuracy of data gained by measurements.

This communication concerns the prestigious award - the Karel Engliš Honorary Medal for Merit in the Social and Economic Sciences - that Bryn Greer-Wootten, Professor Emeritus at York University in Toronto and the Editor-in-Chief of the Moravian Geographical Reports (MGR), received from the Czech Academy of Sciences in2018. The article contains the most important and interesting points from the Laudation by Professor Radim Blaheta (Chair of the Institute of Geonics’ Institutional Board and the previous Director of the Institute), the Response by Professor Greer-Wootten, and the Closing Speech by Bohumil Frantál (Executive Editor of MGR), which were presented during the award ceremony on August 28, 2018 at the historic Löw-Beer Villa in Brno, Czech Republic.

The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.

As an alternative to basic two-level and multilevel iteration preconditioners for elliptic partial differential equations, it is shown that low-rank approximations, based on approximate eigenvectors to the largest eigenvalues of the inverse two-level Schur complement matrix, can give arbitrarily accurate preconditioners that hold uniformly with respect to mesh sizes. The methods are particularly efficient for problems with multiple right hand sides.

UNI-DEM is a large-scale environmental model described by a non-linear system of partial differential equations (PDEs) and used in many studies of air pollution levels in different European countries. The discretization of UNI-DEM leads to a long series of huge computational tasks, because it is necessary to run the discretized model with many different scenarios during long time-periods of many consecutive years. Therefore, both the storage requirements and the computational work are enormous. We had to resolve four difficult problems in the efforts to perform successfully the required simulations. More precisely, we had to do the following: We use several runs over sixteen consecutive years and with fourteen scenarios. Our main purpose will be to show the long-range transport of potentially dangerous air pollutants to Bulgaria.

The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities over parts of the boundary and Tikhonov regularization. To include uncertainties in observed values, Bayesian inversion is also considered in order to obtain a statistical description of unknown material parameters from sampling provided by the Metropolis-Hastings algorithm accelerated by using the stochastic Galerkin method. The connection between Bayesian inversion and Tikhonov regularization and advantages of each approach are also discussed.

The paper concerns development of highly parallelizable preconditioners for solving nonstationary Darcy flow problems. The discretization of the solved problem is done by mixed finite elements in space and by first order implicit Euler discretization in time. The systems with generalized saddle point matrices, which appear in each time step of the implicit Euler method, are then solved by FGMRES method with a block type preconditioner. Moreover, highly parallelizable, one-level additive Schwarz method is used for preconditioning of the velocity block. Both analysis and numerical experiment show that this application of the Schwarz method is highly efficient for a class of flow problems with parameters corresponding to many applications in geosciences.

The paper addresses the construction of parallel iterative solvers for problems of elasticity and poroelasticity. It is shown that such solvers can be built on the basis of conjugate gradient (CG) or another Krylov space iterative method with preconditioning by one- or two-level additive Schwarz methods. The special points of interest are efficient implementation of the two-level Schwarz method on supercomputers and new application of the Schwarz method in three-field poroelasticity formulated in displacements, fluid velocities and pressures.

Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.