Full Tensor Research Articles

A weak subducting slab at intermediate depths below northeast Japan.

Knowledge of the state of stress in subducting slabs is essential for understanding their mechanical behavior and the physical processes that generate earthquakes. Here, we develop a framework which uses a high-resolution focal mechanism catalog to determine the change in the position of the neutral plane before and after the M9 Tohoku-oki earthquake to determine that the deviatoric stress within the slab at intermediate depths must be very low (∼1 MPa). We show that by combining the static stress calculated from coseismic slip distributions with the stress orientations before and after the mainshock, we can determine the full deviatoric stress tensor within the subducting slab at intermediate depths. These results preclude earthquake source mechanisms that require large background driving stresses, favoring a mechanically weak subducting slab, thus providing quantitative constraints on the physical processes that generate intermediate-depth earthquakes.

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ( $E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ( $E(k) \sim k^4$ ). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

An effective multiphysics toolkit for lithium prospecting: From geophysics to the static reservoir model in the Pozuelos salt flat, Argentina

Energy transition drives the energy sector to renewable energy and electrification, being the critical minerals key players in the industrial development map. They comprise rare-earth elements and 35 other elements, including lithium, which holds 60% of its world reserves in the so-called lithium triangle located in Argentina, Bolivia, and Chile. The low electrical resistivities, variations in salt concentrations, low acoustic impedances, and dynamics of the hydrogeologic system make brine monitoring a complex geophysical exploratory problem. So, the objective is to find a suitable combination of geophysical techniques that fit the lithium exploration objectives, which are the characterization of the salt flat in-depth, fluid detection, basement delineation, definition of the main structures and main faults, and detection of semifresh water aquifers that contribute to its recharge and that are key to the reservoir water balance of an endorheic basin, which has the resource in solution. For this purpose, the evaluation of several prospecting methods in different salt flats was executed, concluding that full tensor magnetotellurics (MT), electrical resistivity tomography, and gravity comprise a toolkit that fits the objectives set. The methodology was validated at the Pozuelos salt flat. The results show that the fresh water-brines contact and the recharge system were well-defined and imaged by ERT. The full tensor MT detected two ultraconductive units: a shallower multilayer system saturated with brines, has a 400 m thickness, whereas the deeper unit has a 500 m thickness. Both MT and gravity characterized the basement, and gravity successfully delineated the main structures. The geophysical interpretation is in concordance with shallow and deep exploration wells. Finally, the integration of geophysical and well data allowed the construction of a 3D static reservoir model that finds the deepest basement area at approximately 900 m depth and discriminates eight lithofacies.

Measuring texture-component-dependent stress of CuZn39Pb2 by neutron diffraction

Understanding the micromechanical behavior of polycrystalline material is pivotal for regulating its mechanical performance and widening its application. Taking advantage of its non-destructive nature, the neutron diffraction technique has been widely applied to investigate the micromechanical behaviors, usually at the resolution of grains sharing the same diffraction plane. This work employs a newly developed technic of the texture-component-dependent (TCD) in-situ neutron diffraction method to obtain the full strain/stress tensor of a textured CuZnPb alloy at the resolution of individual crystallographic orientation. The variation of the internal stresses and lattice strains over the grains that share the same diffraction plane has been successfully captured by the TCD method. According to the results of in situ neutron diffraction, Copper ({-1–1–2}<-1–11>) possesses the highest lattice stress while Cube ({010}<100>) and Goss ({110}<001>) bear the lowest stress of 370 MPa. In parallel, the micromechanical response of the texture components is modeled by the elastic visco-plastic self-consistent (EVPSC) model. The simulated results are in reasonable agreement with the corresponding experiments in loading direction, while the lateral stress exhibits some deviation. By crystal plasticity finite element modeling, the deviation is related to the neighbor grain which affect more significantly the lateral stress than the material parameters. The full tensor of stress within the individual crystallographic orientation measured by TCD method gives more insight into the crystal plasticity modeling.

New quadratic/serendipity finite volume element solutions on arbitrary triangular/quadrilateral meshes

AbstractBy postprocessing quadratic and eight‐node serendipity finite element solutions on arbitrary triangular and quadrilateral meshes, we obtain new quadratic/serendipity finite volume element solutions for solving anisotropic diffusion equations. The postprocessing procedure is implemented in each element independently, and we only need to solve a 6‐by‐6 (resp. 8‐by‐8) local linear algebraic system for triangular (resp. quadrilateral) element. The novelty of this paper is that, by designing some new quadratic dual meshes, and adding six/eight special constructed element‐wise bubble functions to quadratic/serendipity finite element solutions, we prove that the postprocessed solutions satisfy local conservation property on the new dual meshes. In particular, for any full anisotropic diffusion tensor, arbitrary triangular and quadrilateral meshes, we present a general framework to prove the existence and uniqueness of new quadratic/serendipity finite volume element solutions, which is better than some existing ones. That is, the existing theoretical results are improved, especially we extend the traditional rectangular assumption to arbitrary convex quadrilateral mesh. As a byproduct, we also prove that the new solutions converge to exact solution with optimal convergence rates under and norms on primal arbitrary triangular/quasi–parallelogram meshes. Finally, several numerical examples are carried out to validate the theoretical findings.

Indirect interaction of 13C nuclear spins in diamond with NV centers: simulation of the full J-coupling tensors

Recent experiments on the detection, imaging, characterization and control of multiple 13C nuclear spins, as well as of individual 13C–13C dimers in diamond using a single nitrogen-vacancy (NV) center as a sensor, along with the impressive progress in increasing the spectral resolution of such sensor (up to sub-Hertz), have created a request for detailed knowledge of all possible spin interactions in the studied systems. Here, we focus on the indirect interaction (J-coupling) of 13C nuclear spins in diamond, which was not previously taken into account in studies of NV centers. Using two different levels of the density functional theory (DFT), we simulated the full tensors nJKL (K, L = X, Y,Z), describing n-bond J-coupling of nuclear spins 13C in H-terminated diamond-like clusters C10H16 (adamantane) and C35H36, as well as in the cluster C33[NV−]H36 hosting the negatively charged NV− center. We found that, in addition to the usually considered isotropic scalar nJ-coupling constant, the anisotropic contributions to the nJ-coupling tensor are essential. We also showed that the presence of the NV center affects the J-coupling characteristics, especially in the case of 13C–13C pairs located near the vacancy of the NV center.

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

AbstractWe develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell‐centered finite volume and node‐based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all‐way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. We identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

Expected Precision of Gravity Gradient Recovered from Ka-Band Radar Interferometer Observations and Impact of Instrument Errors

Full tensor of gravity gradients contains extremely large amounts of information, which is one of the most important sources for research on recovery seafloor topography and underwater matching navigation. The calculation and accuracy of the full tensor of gravity gradients are worth studying. The Ka-band interferometric radar altimeter (KaRIn) of surface water and ocean topography (SWOT) mission enables high spatial resolution of sea surface height (SSH), which would be beneficial for the calculation of gravity gradients. However, there are no clear accuracy results for the gravity gradients (the gravity gradient tensor represents the second-order derivative of the gravity potential) recovered based on SWOT data. This study evaluated the possible precision of gravity gradients using the discretization method based on simulated SWOT wide-swath data and investigated the impact of instrument errors. The data are simulated based on the sea level anomaly data provided by the European Space Agency. The instrument errors are simulated based on the power spectrum data provided in the SWOT error budget document. Firstly, the full tensor of gravity gradients (SWOT_GGT) is calculated based on deflections of the vertical and gravity anomaly. The distinctions of instrument errors on the ascending and descending orbits are also taken into account in the calculation. The precision of the Tzz component is evaluated by the vertical gravity gradient model provided by the Scripps Institution of Oceanography. All components of SWOT_GGT are validated by the gravity gradients model, which is calculated by the open-source software GrafLab based on spherical harmonic. The Tzz component has the poorest precision among all the components. The reason for the worst accuracy of the Tzz component may be that it is derived by Txx and Tyy, Tzz would have a larger error than Txx and Tyy. The precision of all components is better than 6 E. Among the various errors, the effect of phase error and KaRIn error (random error caused by interferometric radar) on the results is greater than 2 E. The effect of the other four errors on the results is about 0.5 E. Utilizing multi-cycle data for the full tensor of gravity gradients recovery can suppress the effect of errors.

Deep Structure of the Santos Basin, Offshore Brazil From 3D Inversion of magnetotelluric Data

AbstractThe relationship between deep crustal structure and the deformation in the overlying sedimentary wedge in Santos basin, Brazil is not well understood, and the origin and evolution of the salt‐related “Albian Gap (AG)” remain a topic of debate. We investigate the deep structure using three‐dimensional inversion of full tensor marine magnetotelluric (MT) data (of 10−1 to 104 s period bandwidth) from 92 stations along three NW–SE lines in 50–1,700 m water depth, one crossing the Cretaceous hinge line (CHL), AG, and Cabo Frio Fault (CFF). The geological validity of the resulting MT resistivity models was determined using resistivity logs from 11 wells and seismic data. The model shows two regionally persistent electrically conductive layers (C2 and C3) related to key Cenozoic and Cretaceous unconformities in the upper part of the sedimentary wedge. Beneath this wedge, the resistive continental crust is ∼35 km thick across the CHL until the 200 m isobath and thereafter thins rapidly seaward to ∼21 km over a lateral distance of ∼80 km defining a domain of highly extended and faulted crust. Our models show a mantle‐associated basement high and evidence of significant uplift of the lower part of the sedimentary wedge at 100–150 km distance along our central profile which spatially coincides with the AG and a previously proposed Moho high. This implies a mantle‐driven deformation of the crust and basin fill. We propose that mantle flow and magmatism may have played a significant role in the inferred displacement at the AG.

Insights on the state of stress in the mantle beneath Pahala, Hawai‘i

Magma supply rates from the mantle to Hawaiian volcanoes serve as an important control on eruptive behavior at the surface. The Pa ̄hala Sill Complex, a collection of magma-bearing, seismogenic structures at 40 km depth beneath Hawai‘i, presents an opportunity to elucidate interactions between stress and magma transport processes in the mantle. We invert for full moment tensors of sill earthquakes and identify predominantly shear mechanisms with persistent tensile faulting components. Slip occurs in-plane with the sill structures. Pressure axes are radially oriented about a point near Mauna Loa, consistent with a stress field generated by a flexural load. Together, these observations suggest that magma flux through the sill structures generates seismicity by increasing pore pressure and promoting slip. Our results suggest that stress changes in mantle structures may enable fluctuations in magma supply rates to the surface over short timescales.

A Novel Projection-based Embedded Discrete Fracture Model (pEDFM) for Anisotropic Two-phase Flow Simulation Using Hybrid of Two-point Flux Approximation and Mimetic Finite Difference (TPFA-MFD) Methods

This paper presents a novel projection-based embedded discrete fracture model (pEDFM) applicable to general two-phase flow simulation in anisotropic reservoirs for the first time. The novel pEDFM is developed based on hybrid two-point flux approximation and mimetic finite difference (TPFA-MFD) methods, which retains the basic features of two-point flux approximation (TPFA) based generic pEDFM workflow and incorporates new features of mimetic finite difference (MFD) to handle full-tensor permeabilities. This is achieved by introducing the concept of effective connection, formulating additional pressure degrees of freedom for effective connections, assigning effective matrix-matrix (m-m) and matrix-fracture (m-f) connections to the corresponding sides of matrix-cell interfaces, presenting methods corresponding to different types of connections to handle low-conductivity fractures, and further deriving formulas of numerical fluxes for effective connections. The resulting global equation system is solved by a Newton-Raphson nonlinear solver with the temporary discretization of the implicit backward Euler scheme. The 2D and 2.5D numerical examples show the novel pEDFM could achieve the same level of computation accuracy and convergence as the reference discrete fracture model (DFM), while avoiding the gridding difficulty of complex fracture networks. It also significantly outperforms classical EDFM based on MFD and generic pEDFM workflow in the computational accuracy for cases with anisotropic full tensor permeabilities. The novel pEDFM, to our best knowledge, is for the first time proposed and developed for general anisotropic two-phase flow simulation and maybe the numerical simulation framework for multi-phase flow in fractured reservoirs with the best comprehensive performance so far.

Efficient method for estimating the dynamics of the full polarizability tensor during ab initio molecular dynamics simulations

Efficient method for estimating the dynamics of the full polarizability tensor during <i>ab initio</i> molecular dynamics simulations

Improvement of density inversion efficiency with projected gradient method: Application to FTG data

With the development of instruments for measuring Earth's gravity gradient tensor, full tensor gravity (FTG) data can be obtained validly and accurately. The highly precise performance of FTG data ensures that they can play an important role in many domains. Generally, FTG data can be acquired from airborne platform, and large-scale data can be obtained by long term observations. For this type of data, research methods for large data processing are very important. Three-dimensional data inversion is an effective and significant method for the quantitative interpretation of FTG data, which has received much attention. Large-scale data inversion is inevitable, and may consume large amounts of time with increase in the amount of data and model parameters. The main aim of this study is to improve the calculation efficiency of FTG data inversion compared with general conjugate gradient (CG) method. Accordingly, an improved gradient method with projections onto a convex set (the projected gradient method) was applied to accelerate the recovery rate of the sub-surface rock density, and a corresponding preconditioning factor was introduced to further improve the calculation efficiency of inversion. This new projected gradient method can improve the calculation efficiency of large amounts of FTG data, which is very necessary for practical application of FTG data. The application of synthetic FTG data with Gaussian noise and the real data demonstrated the feasibility and application value of the proposed inversion method.

Injection-induced fault slip and associated seismicity in the lab: Insights from source mechanisms, local stress states and fault geometry

Probing source mechanisms of natural and induced earthquakes is a powerful tool to unveil associated rupture kinematics. The source processes of failure and slip instability driven by stress loading are affected by fault geometry, but the source ruptures of injection-induced seismicity in relation to fault structures and local stress states remain poorly understood. We have conducted a series of fault reactivation and slip experiments on sandstone samples containing faults with different surface roughness (smooth saw-cut fault and fractured rough fault). We impose progressive fluid injection to induce fault slip, and simultaneously monitor the associated acoustic emission (AE) activity. Using high-resolution AE recordings, we perform full moment tensor inversion of all located AE sources, and investigate the changes of AE source characteristics associated with induced fault slip and their relation to fault roughness. For the complex and rough fault, we observe significant non-double-couple components of AE sources and a high degree of focal mechanism heterogeneity. The temporal changes of AE mechanisms associated with injection-induced fault slip on the smooth fault reveal increasing proportions of double-couple components and decreasing variability of AE focal mechanisms when approaching the onset of slip events. The observed inconsistency between the nodal planes of AE sources and the macroscopic fault plane orientation is attributed to the development of secondary fracture networks surrounding the principal slip surface. We analyze changes in the magnitude-frequency characteristics and source mechanisms of AEs with fault-normal distance, showing that for the smooth (mature) fault, Gutenberg–Richter b-value of on-fault seismicity is lower and focal mechanisms are less heterogeneous, compared to off-fault seismicity. Our results emphasize the important role of roughness-related changes in local fault geometry and associated stress heterogeneity for source mechanisms and rupture kinematics of injection-induced seismicity.

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Quantifying uncertainties in direct numerical simulations of a turbulent channel flow

Direct numerical simulation (DNS) provides unrivalled levels of detail and accuracy for simulating turbulent flows. However, like all numerical methods, DNS is subject to uncertainties arising from the numerical scheme and input parameters (e.g. mesh resolution). While uncertainty quantification (UQ) techniques are being employed more and more to provide a systematic analysis of uncertainty for lower-fidelity models, their application to DNS is still relatively rare. In light of this, the aim of this work is to apply UQ and sensitivity analysis to the DNS of a canonical wall-bounded turbulent channel flow at low Reynolds number (Reτ=180). To compute the DNS, Incompact3d – a highly scalable open-source framework based on high-order compact finite differences and a spectral Poisson solver – is used as a black-box solver. Stochastic collocation is used to propagate the input uncertainties through Incompact3d to the output quantities of interest (QOIs). To facilitate the non-intrusive forward UQ analysis, the open-source EasyVVUQ package is used to provide integrated capability for sampling, pre-processing, execution, post-processing, and analysis of the computational campaign. Three separate UQ campaigns are conducted. The first two examine the effect of domain size and the numerical parameters (e.g. mesh resolution, time step, sample time), respectively, and adopt Gaussian quadrature rules combined via tensor products to sample the multi-dimensional input space. Finally, the third campaign investigates the performance of a dimension-adaptive sampling strategy that significantly reduces the computational cost compared to the full tensor product approach. The analysis focuses on the cross-channel statistical moments of the QOIs, as well as local and global sensitivity analyses to assess the sensitivity of each QOI with respect to each individual input. This enables an assessment of the robustness and sensitivity of DNS to the user-defined numerical parameters for wall-bounded turbulent flows, and provides an indication of suitable ranges for defining the values of these parameters.

A non-local grouping tensor train decomposition model for travel demand analysis concerning categorical independent variables

With the booming of transportation big data, plenty of spatial and temporal features become available for developing travel demand analysis models. However, existing machine learning based travel demand fitting models could face significant model complexity issues once there are multiple discrete/categorical independent variables. This paper embeds a non-local grouping (clustering) process into the tensor train decomposition (NLG-TTD) to characterize the higher-order and nonlinear relationship between categorical variables and travel demand. That is, the transportation dataset with multiple discrete/categorical independent variables and travel demand is treated as a multi-mode tensor, wherein levels of a discrete/categorical variable are regarded as indexes of a mode in the tensor, leading to a “regression on index”. The proposed NLG-TTD model divides the full tensor into non-local sub-tensors, clusters sub-tensors with similarity, conducts tensor train decomposition (TTD) within each cluster, and aggregates cluster-specific learning results. Compared with a conventional TTD that generally works on image completions, NLG-TTD can reveal non-Euclidean and non-linear patterns between categorical/discrete levels in independent variables. It is expected to discover similar travel demand patterns among categorical levels and provide high-level goodness-of-fit. For numerical studies, we use bike-sharing usage data and metro demand data in New York City (NYC), in which several widely-used machine learning models are trained for comparison. The results demonstrate the good performance of the proposed model. Moreover, we apply the NLG-TTD model to analyze and predict the impact of land use shifts on travel demand.

Thermal conductivity of Portlandite: Molecular dynamics based approach

Energy storage provides a greener path of efficient energy utilization. Recent trends of research suggest concrete as a potential thermal energy storage (TES) material. Its cheap commercial availability makes it one of the most deserving candidates. Cement paste is the key glue of concrete, hence performance of its major components in thermal conduction seeks thorough scientific study. Portlandite or calcium hydroxide is the second major component of cement paste, microscopically visible at a scale length of <10−4 m. Molecular dynamics (MD) simulation has been utilized to investigate the thermal transport mechanism of portlandite at an atomistic scale. The thermal conductivity of this component has been computed using three major force fields which are compared with the experimental outcome using modulated differential scanning calorimetry (MDSC). It has been observed that the simulation outcomes are in order with the experimental value but the results are sensitive to the choice of force fields. Excitation of molecules during thermal transport is predominantly governed by lower-frequency molecular vibration indicating the existence of Boson Peaks. This manuscript presents the full thermal conductivity tensor of portlandite along with the possible mechanism associated with thermal transport.

Three-dimensional magnetotelluric imaging of the Edough massif and its overlying formations (Northeast Algeria)

The Edough massif (NE Algeria) is the easternmost coastal crystalline massif of the Maghrebide belt, whose current structural position remains poorly known. Magnetotelluric (MT) data from 15 stations were collected along three profiles across the Edough massif and its neighboring formations in the period range of 0.001–1000 s to assess the deep electrical resistivity structure. A phase tensor dimensionality analysis indicates that the measured data are dominated by 3-D effect of underlying geological structure, thus revealing a complex subsurface structure. A 3-D inversion model was obtained using the full impedance tensor and the vertical magnetic field transfer function including bathymetry and topography. Our preferred 3-D geo-electrical model shows heterogeneous electrical structures and are related to the known geological features of the region. We mainly observe a clear resistivity contrast characterizing the upper/middle crust. The Edough massif appears generally as a homogenous resistive structure. The shallow conductive structures are associated with the Mio-Plio-Quaternary deposits and Flysch units. Most of conductive bodies are likely related to the iron/magnetic anomaly. These may likely correspond to the suture zone. Under the Neogene basin, the high resistivities with a north dipping strong angle may correspond to the African basement.

A low-rank isogeometric solver based on Tucker tensors

We propose an isogeometric solver for Poisson problems that combines (i) low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, (ii) a Truncated Preconditioned Conjugate Gradient solver to keep the rank of the iterates low, and (iii) a novel low-rank preconditioner, based on the Fast Diagonalization method where the eigenvector multiplication is approximated by the Fast Fourier Transform. Although the proposed strategy is written in arbitrary dimension, we focus on the three-dimensional case and adopt the Tucker format for low-rank tensor representation, which is well suited in low dimension. We show by numerical tests that this choice guarantees significant memory saving compared to the full tensor representation. We also extend and test the proposed strategy to linear elasticity problems.