Domain Decomposition Technique Research Articles

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. The presented numerical experiments demonstrate the excellent performance of the proposed methods.

Additive Schwarz preconditioners for a localized orthogonal decomposition method

We investigate a variant of the localized orthogonal decomposition method (Henning and Peterseim, [Multiscale Model. Simul., 11 (2013), pp. 1149–1175] and Målqvist and Peterseim, [Math. Comp., 83 (2014), pp. 2583–2603]) for elliptic problems with rough coefficients. The construction of the basis of the multiscale finite element space is based on domain decomposition techniques, which is motivated by the recent work of Kornhuber, Peterseim, and Yserentant [Math. Comp., 87 (2018), pp. 2765–2774]. We also design and analyze additive Schwarz domain decomposition preconditioners for the resulting discrete problems.

Nonlinearizing Two-parameter Eigenvalue Problems

We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original and the nonlinearized problem theoretically and show how to use the transformation computationally. Special cases of the transformation can be interpreted as a reversed companion linearization for polynomial eigenvalue problems, as well as a reversed (less known) linearization technique for certain algebraic eigenvalue problems with square-root terms. Moreover, by exploiting the structure of the NEP we present algorithm specializations for NEP methods, although the technique also allows general solution methods for NEPs to be directly applied. The nonlinearization is illustrated in examples and simulations, with focus on problems where the eliminated equation is of much smaller size than the other two-parameter eigenvalue equation. This situation arises naturally in domain decomposition techniques. A general error analysis is also carried out under the assumption that a backward stable eigenvalue solver method is used to solve the eliminated problem, leading to the conclusion that the error is benign in this situation.

Response surface-based model updating to detect damage on reduced-scale masonry arch bridge

Response surface (RS) methods, a combination of mathematical and statistical techniques, have been widely used in design optimization, response prediction, and model validation in structural engineering systems. However, its usage in structural damage identification, especially for historic structures has not been quite common. For this purpose, this study attempts to investigate damage detection in a masonry arch bridge. Within the scope of this, a reduced-scale model of a one span historical masonry arch bridge was built in a laboratory environment. To determine the modal parameters of the reduced-scaled bridge model, operational modal analysis (OMA) was performed under ambient vibrations. Signals originated by sensitive accelerometers were collected to quantify the vibratory response of the reduced-scaled model bridge. The experimental natural frequencies, mode shapes, and damping ratios resulting from these measurements were figured out by using the Enhanced Frequency Domain Decomposition (EFDD) technique. The three-dimensional model of the reduced-scale bridge was created in the ANSYS finite element (FE) software program to expose the analytical dynamic characteristics of the bridge model. The results obtained in the experimental application were compared with those of the finite-element analysis of the bridge model. The calibration of the numeric model was utilized depending on the experimental modal analysis results of the reduced-scale bridge by using the RS method. Design of experiments was constructed by using central composite design, and the RS models were generated by performing the genetic aggregation approach. The optimum results between the experimental and numerical analyses were found by using the RS optimization. Then, regional damages created on the scaled model and the changes of dynamic properties of the damaged case were evaluated. The damage location was approximately identified by using the RS method in the calibrated finite-element model. The results demonstrated that the RS-based FE updating approach is an effective way for damage detection and localization in masonry type structures.

Domain decomposition based on the spectral element method for frequency-domain computational elastodynamics

We propose a domain decomposition method based on the spectral element method (DDM-SEM) for elastic wave computation in frequency domain. It combines the high accuracy of the spectral element method and the high degree of parallelism of a domain decomposition technique, which makes this method suitable for accurate and efficient simulations of large scale problems in elastodynamics. In the DDM-SEM, the original large-scale problem is divided into a number of well designed subdomains. We use the spectral element method independently for each subdomain, and the neighboring subdomains are connected by a frequency-domain version of Riemann transmission condition (RTC) for elastic waves. For the proposed method, we can employ the non-conforming meshes and different interpolation orders in different subdomains to maximize the efficiency. By separating the internal and boundary unknowns of each subdomain, an efficient and naturally parallelizable block LDU direct solver is developed to solve the final system matrix. Numerical experiments verify its accuracy and efficiency, and show that the proposed DDM-SEM can be a promising numerical tool for accurately and effectively solving large and multi-scale problems of elastic waves. It is potentially valuable for the frequency domain seismic inversion where multiple source illuminations are required.

A stable RBF partition of unity local method for elliptic interface problems in two dimensions

The interface problems are faced with multiple connected domains and consequently, their solutions or derivatives might be discontinuous. This paper proposes the use of collocation based radial basis function partition of unity method (RBF-PUM) for solving two-dimensional elliptic interface problems. The RBF-PUM is a local method that allows overcoming the high computational cost associated with the global RBF methods. In the RBF-PUM, the domain is split into overlapping patches forming a covering of it. However, this method suffers from instability when the RBF shape parameter ε tends to zero. To overcome this issue, we use the RBF-QR algorithm which offers stable computations for all values of ε and provides higher accuracy. To obtain the appropriate solution in the vicinity of the interface, the domain decomposition technique is used. In this technique, the approximation in each subdomain is built separately, and proper jump conditions are then imposed across the interface. We illustrate how to apply the proposed method to Sturm-Liouville, Sturm-Liouville eigenvalue and elastostatic interface problems. The proposed method in dealing with arbitrary interfaces within different domain sizes is validated. We present some numerical examples in which the results are compared with exact solutions and those provided by other numerical methods.

Damping estimation of a pedestrian footbridge – an enhanced frequency-domain automated approach

Real-time estimates of natural frequencies, mode shapes and damping of a structural system can be interpreted to its structural health. In this regard, real-time estimation of damping ratios for full-scale structures can be useful by itself or in conjunction with real-time estimates of natural frequencies. Such estimates also allow for continuous health monitoring. This paper demonstrates an approach of assessing real-time damping in full scale bridges and demonstrates this on one of the iconic steel bridges in Ireland, the Daly’s “Shaky” bridge. This is the only suspension bridge in the city of Cork, Ireland and renowned in popular culture for its lively behaviour. From existing vibration data evaluated from an image processing technique, the damping estimates of the Daly’s bridge are evaluated based on an automated enhanced frequency domain decomposition (AE-FDD) technique. The method provides accurate estimates of natural frequencies and mode shapes and additionally yields the damping ratio corresponding to each vibration (and/or torsional) mode. This technique of real-time damping estimation can be easily adapted for other full-scale structures in an automated real-time framework.

REEF3D Wave Generation Interface for Commercial Computational Fluid Dynamics Codes

Abstract In recent years, computational fluid dynamics (CFD) developments have shown a trend to combine Reynolds-averaged Navier–Stokes (RANS) CFD simulation with other methods such as wave theories or velocity potential-based numerical wave tanks, in order to reduce to computation costs. This is however not a new approach, and there exists a large amount of literature about domain decomposition techniques describing a two way coupling between the RANS CFD models and other methods. One can also observe an increasing popularity in the use of a less sophisticated technique where different fluid solvers are combined with one-way coupling. In these methods, a predefined solution is provided in the far-field, while a three-dimensional (3D) CFD simulation is applied in a limited zone near the structure. The predefined solution is used to specify the background far-field solution. The published solutions use wave theory or a numerical wave tank where the predefined solution is calculated parallel to the RANS solver. In this way, it is possible to reduce the interpolation inaccuracy and the amount of transferred data to the CFD simulation. The disadvantage of this technique is that the far field solver has to be prepared in order to run in parallel with the CFD solver. Due to the one way coupling, it is possible to predefine this information in tables before the CFD simulation. This technique makes it possible to define a general interface between difference solvers without modifying existing codes. This paper presents such a technique where the predefined solution is stored into files.

VULNERABILITY ASSESSMENT OF A CIVIC TOWER USING AMBIENT VIBRATION TESTS

This paper focuses on the vulnerability assessment of a civic tower built in 1512, which is now considered a national monument. It is the original bell tower of S. Ambrogio church that was destroyed in 1809. Experimental investigations have been carried out on this historical tower. First, detailed investigations have been carried out to identify the geometry of the tower as well as the mechanical features of the constituting materials. Then, ambient vibration tests have been applied using five Micro Electro-Mechanical Systems (MEMS) sensors to detect of the main dynamic features, e.g., modal parameters and damping. Two output-only identification methods, including Frequency Domain Decomposition and Random Decrement Techniques, have been used. The outcomes of the modal identification have been employed to inform the FE model. The numerical analysis can be used for vulnerability assessment, providing a valuable picture of possible damage evolution, tower collapse mechanism, and subsequently, useful hints for the execution of structural retrofitting strategies.

Direct FEM-Domain Decomposition Using Convex-to-Concave Spherical Ports for Space Applications

This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on the analytical manipulation of the generalized scattering matrix obtained from the finite-element method, when concave and convex spherical surfaces are defined as ports. The technique combines: the power of full-wave resolution, the flexibility and speed of the direct domain decomposition techniques and the application of analytical rotations and translations from the addition theorems for spherical vector waves, while keeping the same accuracy as a complete full-wave method since no model simplifications are considered.

Numerical simulation of DIC drying process on matlab distributed computing server

<span>Instant controlled pressure drop, also known as DIC, is one of the drying techniques that has been used for texturing, extracting and drying various food products. Mathematical model has been used to explain the drying process, although most of the studies focused on the statistical regression model approach. Due to the limitations of regression model, which neglects the fundamental of dehydration process, t</span><span>his paper presents the development of mathematical models to detect, solve and visualize the three-dimensional (3D) heat and mass transfer in DIC drying process. </span><span>Finite Difference Method (FDM) with central difference formula is used to discretize the mathematical models. A large sparse of system of linear equation (SLE), which represents the actual drying process, is solved by using some numerical methods, such as Jacobi (JB), Red Black Gauss Seidel (RBGS), Alternating Group Explicit with Douglas (AGED) and Brian (AGEB) methods. Based on the numerical results, high execution time and high computational complexity have been shown. In order to reduce the execution time and computational complexity, the parallel algorithm based on domain decomposition technique has been implemented on the MATLAB Distributed Computing Server (MDCS). The parallel algorithm of the numerical methods was evaluated and compared based on the parallel performance metrics: execution time, speed up, efficiency, effectiveness, temporal performance and granularity. From the parallel performance metrics, it was found that the PAGEB approach had better performance, followed by PAGED, PRBGS and PJB methods.</span>

Mode shape–aided cable force determination using digital image correlation

Assuming the distance between two nodal points of a specific cable vibration mode as the effective length of a pinned–pinned cable, mode shape–aided cable tension estimation methods are employed to estimate the cable force. This article proposes a framework based on digital image correlation technique for remote measurement of the dynamic displacement time history of cables in cable structures. Frequency domain decomposition technique is then used to extract the cable natural frequencies and mode shapes. Identified cable mode shapes are used along with a tensioned pinned–pinned cable model to estimate the cable force. Accuracy of the proposed methodology is investigated using the experimental data coming from a laboratory-scale test setup and hanger cables of a real-world arch bridge.

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation

In this study, a Modified Frequency and Spatial Domain Decomposition (MFSDD) technique is developed for modal parameter identification, using output-only response measurements. According to the presented procedure, the most probable power spectral density matrix of the measured response (output PSD) is updated by a maximum likelihood estimation based on the observed data. Different from the available Frequency Domain Decomposition (FDD) techniques, a prediction error term which is associated with the measurement noise and modelling errors is included in the proposed methodology. In this context, a detailed discussion is provided from various aspects for the effect of measurement noise and modelling errors on the parameter estimation quality. Two numerical and two experimental analysis are conducted in order to demonstrate the effectiveness and accuracy of the proposed methodology under some extreme effects. The obtained results indicate that the proposed method shows very good performance in modal parameter estimation in case of noisy measurements.

A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

A non-overlapping domain decomposition method is proposed to solve large-scale finite element models for the propagation of sound with a background mean flow. An additive Schwarz algorithm is used to split the computational domain into a collection of sub-domains, and an iterative solution procedure is formulated in terms of unknowns defined on the interfaces between sub-domains. This approach allows to solve large-scale problems in parallel with only a fraction of the memory requirements compared to the standard approach which is to use a direct solver for the complete problem. While domain decomposition techniques have been used extensively for Helmholtz problems, this is the first application to aero-acoustics. The optimized Schwarz formulation is extended to the linearized potential theory for sound waves propagating in a potential base flow. A high-order finite element method is used to solve the governing equations in each sub-domain, and well-designed interface conditions based on local approximations of the Dirichlet-to-Neumann map are used to accelerate the convergence of the iterative procedure. The method is assessed on an academic test case and its benefit demonstrated on a realistic turbofan engine intake configuration.

A General Design for a Scalable MPI-GPU Multi-Resolution 2D Numerical Solver

This article presents a multi-GPU implementation of a Finite-Volume solver on a multi-resolution grid. The implementation completely offloads the computation to the GPUs and communications between different GPUs are implemented by means of the Message Passing Interface (MPI) API. Different domain decomposition techniques have been considered and the one based on the Hilbert Space Filling Curves (HSFC) showed optimal scalability. Several optimizations are introduced: One-to-one MPI communications among MPI ranks are completely masked by GPU computations on internal cells and a novel dynamic load balancing algorithm is introduced to minimize the waiting times at global MPI synchronization barriers. Such algorithm adapts the computational load of ranks in response to dynamical changes in the execution time of blocks and in network performances; Its capability to converge to a balanced computation has been empirically shown by numerical experiments. Tests exploit up to 64 GPUs and 83M cells and achieve an efficiency of 90 percent in weak scalability and 85 percent for strong scalability. The framework is general and the results of the article can be ported to a wide range of explicit 2D Partial Differential Equations solvers.

Dynamic Identification as a Tool to Constrain Numerical Models for Structural Analysis of Historical Buildings

In recent few decades, operational modal analysis (OMA), also known as output-only or ambient vibration test (AVT), has become a powerful tool for a wide range of applications in the field of civil engineering. The output-only modal test represents an effective alternative to forced vibration techniques when historical structures are investigated. This method takes advantages from natural sources of vibration (wind, traffic, etc.) instead of having to shake the structure artificially. This paper shows how the dynamic characteristics of a building (i.e. frequency, modal shapes and damping ratios) can be automatically identified by enhanced frequency domain decomposition (EFDD) technique. The assessment of the dynamic characteristics is performed analyzing the Baptistery of San Giovanni in Firenze (Italy) where a network of seismic sensors was temporarily installed. The modal parameters are used to calibrate a 3D finite element (FE) numerical model, by using a genetic algorithm (GA). This procedure allows to obtain accurate and robust model capable to reproduce the actual dynamic behavior of the structure by minimizing the uncertainties related to the mechanical parameters. This paper, providing an illustrative case study in the field of health monitoring of monumental structures, confirms that the OMA technique is able to derive effective information on the dynamic behavior of the analyzed building, which is useful to tune reliable and robust numerical models to be employed for structural analysis.

Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences

Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical schemes based on a spherical mesh. Despite its orthogonality property, the polar (latitude-longitude) mesh is ill suited for computation because of the singularity on the polar axis, leading to a highly non-uniform distribution of zone sizes. The consequences are (a) loss of accuracy due to large variations in zone aspect ratios, and (b) poor computational efficiency from a severe limitations on the time stepping. Geodesic meshes, based on a central projection using a Platonic solid as a template, solve the anisotropy problem, but increase the complexity of the resulting computer code. We describe a new finite volume implementation of Euler and MHD systems of equations on a triangular geodesic mesh (TGM) that is accurate up to fourth order in space and time and conserves the divergence of magnetic field to machine precision. The paper discusses in detail the generation of a TGM, the domain decomposition techniques, three-dimensional conservative reconstruction, and time stepping.

Model updating of a reduced-scaled masonry bridge by using response surface method

Historical structures reflect the historical and cultural properties of countries and also contributes to the economy in terms of cultural tourism. Therefore, it is important to understand the structural behavior of these kinds of structures under dynamics loads such as earthquakes, etc. to protect and transfer them safely to future generations. For this reason, this study aims to investigate the dynamic behavior of a reduced-scale one-span masonry arch bridge constructed in laboratory conditions by performing experimental and numerical analysis. Operational Modal Analysis (OMA) Technique was performed under ambient vibrations for experimental study to determine modal parameters of the reduced-scaled bridge model. Sensitive three-axial accelerometers were located on critical points on the bridge span and signals originated by accelerometers were collected to quantify the vibratory response of the scale bridge model. The experimental natural frequencies, mode shapes and damping ratios resulting from these measurements were figured out by using Enhanced Frequency Domain Decomposition (EFDD) technique. ANSYS software was utilized to carry out 3D finite element (FE) modeling of the reduced-scale masonry bridge and determine the natural frequencies and mode shapes of the bridge numerically. Experimental results were compared with FE analysis results of the bridge. Significant differences appeared when comparing the results of the experimental and numerical with the initial conditions. Therefore, the finite element model is calibrated by using the response surface (RS) method according to the experimental results to minimize the uncertain finite element modeling parameters of the reduced-scale bridge model such as material properties.

Investigating on multi-RANS models coupling simulation for flow mixing experiments

Prediction and analysis of coolant flow and mixing problems in the reactor pressure vessel (RPV) are some of the most critical studies to ensure system safety and balance of nuclear power plant. The flow mixing problem in the reactor primary system with complicated interior structure is a large domain three-dimensional problem. In this paper, we investigated the performance of utilizing multiple RANS models (MRANS) coupling method in the computational fluid dynamics (CFD) code ANSYS FLUENT to study flow mixing. Based on the domain decomposition technique, the 2-equation and 7-equation RANS models were coupled and applied to simulate the flow mixing phenomenon in the Rossendorf Coolant Mixing Model (ROCOM) test facility. First, a CFD model of ROCOM was developed, and the explicit domain decomposition coupling simulation was achieved with a user-defined Python control program. To ensure the best CFD model was utilized, three different turbulence models and varying resolution grids were used for turbulence model feasibility analysis and grid sensitivity testing. Then the applicability of MRANS coupling method was evaluated by comparing the results from the MRANS simulations with those obtained from flow mixing experiments. In addition, single and MRANS model simulation results were compared. Results show good agreements between the MRANS coupling simulations and the experimental data. Compared with overall simulations by single RANS models, the MRANS coupling method also have superior performance in accuracy and efficiency for the CFD simulation study of mixing phenomena in the reactor primary coolant system.

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures.

We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals (N ∼ 1010). KITE’s core is written in C++, with a versatile Python-based interface, and is fully optimized for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green’s functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution. Several functionalities are demonstrated, ranging from simulations of local density of states and photo-emission spectroscopy of disordered materials to large-scale computations of optical conductivity tensors and real-space wave-packet propagation in the presence of magneto-static fields and spin–orbit coupling. On-the-fly calculations of real-space Green’s functions are carried out with an efficient domain decomposition technique, allowing KITE to achieve nearly ideal linear scaling in its multi-threading performance. Crystalline defects and disorder, including vacancies, adsorbates and charged impurity centres, can be easily set up with KITE’s intuitive interface, paving the way to user-friendly large-scale quantum simulations of equilibrium and non-equilibrium properties of molecules, disordered crystals and heterostructures subject to a variety of perturbations and external conditions.