In this paper, we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two applications: the construction of efficient quasi-interpolation schemes and the numerical solution of elliptic problems using the isogeometric Galerkin method.

In this paper we develop and analyze several preconditioners for the linear systems arising from discretized poroelasticity problems. The preconditioners include one block preconditioner for the two-field Biot model and several preconditioners for the classical three-field Biot model. We manage to analyze these different preconditioners under a same theoretical framework and show that all of them are

We propose a mixed stress-displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von Mises plasticity. The discretization is based on isogeometric analysis (IGA) with non-uniform rational B-Splines (NURBS) as basis functions. As compared to conventional IGA Galerkin formulations, isogeometric collocation methods offer a high potential of

Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for design-dependent loads. First, a mathematical model of the optimization problem is established with the structural compliance minimization as the objective function and the structural volume fraction as the design constraint. By converting the line integrals into

An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyses in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which

In this note we will explore some applications of the recently constructed piecewise affine, H1-conforming element that fits in a discrete de Rham complex (Christiansen and Hu, 2018). In particular we show how the element leads to locking free methods for incompressible elasticity and viscosity robust methods for the Brinkman model.

An efficient numerical scheme at the crossroad of Fourier based methods and boundary element methods is derived to upscale the permeability of porous media from Stokes flow within the pore space. The method relies on a variational framework which involves trial force fields and the Green function. The discretization of the trial force fields is carried out on a uniform grid, which allows for the use

Different from large deflection analyses of plates and shells, for analysis of an isotropic membrane structure a form finding procedure is first performed to find the new geometry of membrane. With this new geometry, large deflection analysis is conducted and the membrane works in a pure membrane state. In the conventionally numerical approaches for analysis of membranes, form finding and large deflection

The semiclassical Schrödinger equation with time-dependent potentials is an important model to study electron dynamics under external controls in the mean-field picture. In this paper, we propose two multiscale finite element methods to solve this problem. In the offline stage, for the first approach, the localized multiscale basis functions are constructed using sparse compression of the Hamiltonian

This paper proposes a topology optimization method that is capable of simultaneous design for structural topology, stiff material (i.e. fiber) layout, and its orientations in functionally graded anisotropic composite structures. Functionally graded composites are inhomogeneous materials with continuously varying spatial composition. The spatial variation in material properties might enable better performance

Modal metamodels can be effectively used as surrogates for expensive simulations in structural dynamics analysis with parametric variations. However, in the case of a system with clustered eigenvalues, e.g., a structure exhibiting symmetry or periodicity, mode interactions due to parametric variations are challenging to handle. Clustered eigenvalues are potentially associated with high sensitivity

An alternative to three existing types of mesh (structured grid, unstructured grid, and gridfree points) — general mesh — is proposed for Computational Fluid Dynamics (CFD). It includes three existing ones and the arbitrary mixing of mesh and points by using a unified framework. Different from the traditional hybrid grid/gridfree methods requiring separate numerical schemes for the respective grid

Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration

In this work, the potential of carrying out inverse problems with linear and non-linear behaviour is investigated using deep learning methods. In inverse problems, the boundary conditions are determined using sparse measurement of a variable such as velocity or temperature. Although this is mathematically tractable for simple problems, it can be extremely challenging for complex problems. To overcome

This paper focuses on viral decontamination by ultraviolet (UV) irradiation technologies. This work develops an efficient and rapid computational method to simulate a UV pulse in order to ascertain the decontamination efficacy of UV irradiation for a surface. It is based on decomposition of a pulse into a group of rays, which are then tracked as they progress towards the target contact surface. The

This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate available, yet incomplete, physics knowledge (e.g., laws of physics, scientific principles) into deep long short-term memory (LSTM) networks, which constrains and boosts the learning within a feasible solution space. The

In a previous work, embedded ensemble propagation was proposed to improve the efficiency of sampling-based uncertainty quantification methods of computational models on emerging computational architectures. It consists of simultaneously evaluating the model for a subset of samples together, instead of evaluating them individually. A first approach introduced to solve parametric linear systems with

Inspired by venation patterns of leaves, the new polyline-based core sandwich structures (PCSSs) are developed in this paper. A novel approach is proposed under explicit topology optimization framework based on surrogate-assisted evolutionary algorithm. Specifically, a multi-component topology description function is defined to characterize the shapes of polyline-based cores, and therefore the dimension

Ideas from the mathematical theory of optimal transport have recently been transferred to the micromechanics of polycrystalline materials, leading to fast methods for generating polycrystalline microstructures with grains of prescribed volume fraction in terms of centroidal Laguerre tessellations. In this work, we improve the state of the art solvers. For a given set of seeds and corresponding volume

Based on a formulation on the special Euclidean group SE(3), a geometrically exact thin-walled beam with an arbitrary open cross-section is proposed to deal with the finite deformation and rotation issues. The beam strains are based on a kinematic assumption where warping deformation and Wagner effects are included such that the nonlinear behavior of a thin-walled beam is predicted accurately, particular

Finite element simulations of frictional multi-body contact problems via conformal meshes can be challenging and computationally demanding. To render geometrical features, unstructured meshes are often generated via a trial-and-error procedure. This treatment also unavoidably increases the degrees of freedom and makes the construction of slave/master pairs cumbersome. In this work, we introduce an

Phase-field models for fracture have gained exceptional popularity in the last couple of decades and have been extended into areas well beyond brittle quasi-static fracture propagation to ductile, dynamic, or hydraulic fracturing. Despite the significant theoretical advancements in these more complex physical settings, little attention has been paid to the quantification of crack opening displacement

This paper considers topology optimization approaches where the geometry is described by a level set method and the system’s response is discretized on nonconforming meshes while providing a crisp definition of interface and external boundaries. Since the interface is explicitly tracked, the elements intersected by the interface are divided into sub-elements to which a phase needs to be assigned. Due

In recent years, stochastic simulation has obtained increasing attention in geomechanics as it allows to consider uncertainties in geomaterials’ properties. Spatial uncertainties may influence simulation results and lead to either unsafe or uneconomic designs. By implementing stochastic random field algorithms in Finite-Element simulations, the impact of such uncertainty can be integrated in the simulation

A flexible, general and stable mixed formulation is developed to model distributed cracking in cohesive grain-based materials in the framework of the extended/generalized finite element method. The displacement field is discretized on each grain separately, and the continuity of the displacement and traction fields across the interfaces between grains is enforced by Lagrange multipliers. The design

While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the material is not size-dependent. Yet, a length scale parameter must be introduced to these models to enable sharp cracks properly represented by a regularized implicit

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase

As a typical convex model, the parallelepiped plays an important role in the non-probabilistic uncertainty quantification with simultaneous dependent and independent variables. To overcome the complexity of the conventional geometric design-based method, this paper proposes a more efficient sample-driven procedure to construct the explicit mathematical expression of parallelepiped model. Instead of

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this can at best be performed semi-manually. We propose a fully automated and topologically accurate approach to synthesise a structurally-sound parametric

Space fractional diffusion models generally lead to dense discrete matrix operators, which lead to substantial computational challenges when the system size becomes large. For a state of size N, full representation of a fractional diffusion matrix would require O(N2) memory storage requirement, with a similar estimate for matrix–vector products. In this work, we present H2 matrix representation and

We analyze the Biot system solved with a fixed-stress split, Enriched Galerkin (EG) discretization for the flow equation, and Galerkin for the mechanics equation. Residual-based a posteriori error estimates are established with both lower and upper bounds. These theoretical results are confirmed by numerical experiments performed with the Mandel’s problem. The efficiency of these a posteriori error

We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection–reaction equations discretized by the finite element method. This change of variable confines the concentration below an upper bound in a very natural way. For the non-negativity constraint, we propose to use a discontinuity capturing method defined on the reference element that

In this paper, the first self-adaptive deep learning algorithm is proposed in details to accelerate flash calculations, which can quantitatively predict the total number of phases in the mixture and related thermodynamic properties at equilibrium for realistic reservoir fluids with a large number of components under various environmental conditions. A thermodynamically consistent scheme for phase equilibrium

The promising phase-field method has been intensively studied and demonstrated to provide reliable predictions of structural failure. Motivated by experimental findings, the fracture patterns within several engineering materials are characterized as anisotropic, and are governed by the elastic and the fracture properties simultaneously. In this work, a physically anisotropic phase-field model is developed

This paper presents a nonlinear multiscale approach for periodic structures in the quasi-static, small strain regime. The approach consists in combining a domain decomposition method in which interface conditions are established through a “fictitious” frame with reduced-order modeling (ROM). We propose to approximate interface displacements, subdomain displacements and Lagrange Multipliers as linear

A finite volume approximation of the scalar hyperbolic conservation law or advection–diffusion equation is given. In the context of the method of lines, the space discretization uses weighted essentially non oscillatory (WENO) reconstructions with adaptive order (WENO-AO), and the time evolution uses implicit Runge–Kutta methods. Therefore the timestep may be larger than the CFL timestep. To reduce

This work is an extension of the ideas in Averweg et al. (2019) with the focus on a detailed investigation of implicit time discretization schemes to model instationary fluid flow, based on the incompressible Navier–Stokes equations, and linear elastodynamic structural behavior. The variational approaches for fluid and solid mechanics are based on a mixed least-squares finite element method. The L2-norm

In order to efficiently solve nonlinear transient heat conduction problem, a method combining the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) is proposed to establish the nonlinear reduced-order model, and the implementation of the reduced-order model makes fast numerical simulation possible in engineering field. Transient heat conduction problems

A residual-based variational multi-scale (VMS) modeling framework is applied to simulate atmospheric flow over complex environmental terrains. The VMS framework is verified and validated using two test cases using linear finite element (FEM) and quadratic non-uniform rational B-spline (NURBS) discretizations. First, the flow over the 3D, axisymmetric Gaussian hill (normally distributed surface) is

We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, while the a-priori error is estimated to guarantee linear convergence of the H1 error. In the adaptive mesh refinement, efficient estimation

In this work, we present a higher-order nonlocal continuum theory of a recently developed updated Lagrangian particle hydrodynamics (ULPH) (see: Tu and Li, 2017 and Yan et al., 2019) and its applications to multiphase flows. The original nonlocal differential operators used in ULPH have only the first-order accuracy, and they may not be able to simulate some complicated and delicate three-dimensional

In the present work the multi-phase SPH model presented in Grenier et al. (2009) is considered and extended through the inclusion of a diffusive term in the continuity equation. The latter based on the δ-SPH model of Antuono et al. (2012), allows to improve the evaluation of the pressure field, removing numerical noise and improving also the particles spatial distribution. The time stepping and the

It is well known that for problems approaching incompressible limits, standard finite element approaches suffer from suboptimal convergence due to a phenomenon known as locking. We analyze this phenomenon and present a robust generalized finite element formulation that enables optimal solution convergence. This approach is explored for the two-dimensional incompressible elasticity equations with a

In this paper we present a finite-element based reduced order model and, in particular, we consider two aspects related to the introduction of inter-element boundary terms in the formulation. The first is a domain decomposition strategy in which the transmission conditions involve boundary terms to account for non-matching meshes and discontinuous physical properties. The second is a coarse mesh hyper-reduction

Silica-based glass may possess paradoxically high resistance to hypervelocity impact due to the experimentally observed phase change emanating from high pressure characteristic to hypervelocity impact combined with irreversible densification of the material, which leads to a highly efficient kinetic energy-absorption mechanism. In order to capture this extraordinary behavior of silica glass in hypervelocity

This paper aims to provide new insights into model calibration, which plays an essential role in improving the validity of Modeling and Simulation (M&S) in engineering design and analysis. Various existing model calibration approaches including the direct Bayesian calibration method, the well-known Kennedy and O’Hagan (KOH) framework and its variants, and the optimization-based calibration method,

A novel second-order reduced homogenization (SORH) approach is introduced for analyzing dynamic thermo-mechanical coupling problems in axisymmetric inelastic structures with periodic micro-configuration. The axisymmetric heterogeneous structures are periodically distributed in radial and axial directions and homogeneous distribution in circumferential directions. Firstly, the nonlinear coupled thermo-mechanical

We analyze a hybridizable discontinuous Galerkin (HDG) method for the time harmonic Maxwell’s equations arising from modeling photovoltaic solar cells. The problem is set in an inhomogeneous domain with a polyhedral connected boundary and the divergence-free condition is imposed using a Lagrange multiplier. We prove the HDG scheme is well-posed up to some frequencies and derive a stability estimate

The simulation of multiscale problems remains a challenge in many problems due to the complex interaction between the resolved and unresolved scales. This work develops a coarse-grained modeling approach for Galerkin discretizations by combining the Variational Multiscale decomposition and the Mori–Zwanzig (M–Z) formalism. An appeal of the M–Z formalism is that – akin to Green’s functions for linear

The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche’s method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable method. In this contribution we extend the multimesh finite element method to the Navier–Stokes

Constrained mixture models of soft tissue growth and remodeling can simulate many evolving conditions in health as well as in disease and its treatment, but they can be computationally expensive. In this paper, we derive a new fast, robust finite element implementation based on a concept of mechanobiological equilibrium that yields fully resolved solutions and allows computation of quasi-equilibrated

The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this paper, we reformulate the problem based on the temperature field in the skeleton and derive an equation

Thickness-controllable topology optimization is presented for three-dimensional problems using moving morphable patches. Geometric features of triangular patches were employed as design variables to enable the representation of shell-like members and beam or bar members with a small number of design components. The minimum thickness for mean compliance minimization problems can be controlled simply

In this work a new methodology for both the nearly and fully incompressible transient finite strain solid mechanics problem is presented. To this end, the momentum equation is complemented with a constitutive law for the pressure which emerges from the deviatoric/volumetric decomposition of the strain energy function for any hyperelastic material model. The incompressible limit is attained automatically

The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy’s law). The numerical challenge for this model is the designing of a numerical scheme which is stable for both the Stokes-dominated (high permeability) and the Darcy-dominated

Today numerical simulation is indispensable in industrial design processes. It can replace cost and time intensive experiments and even reduce the need for prototypes. While products designed with the aid of numerical simulation undergo continuous improvement, this must also be true for numerical simulation techniques themselves. Up to date, no general purpose numerical method is available which can

This work presents a Fluid–Structure Interaction framework for the robust and efficient simulation of strongly coupled problems involving arbitrary large displacements and rotations. We focus on the application of the proposed tool to lightweight membrane-like structures. Nonetheless, all the techniques we present in this work can be applied to both volumetric and volumeless bodies. To achieve this

This paper focuses on density-based topology optimization and proposes a combined method to simultaneously impose Minimum length scale in the Solid phase (MinSolid), Minimum length scale in the Void phase (MinVoid) and Maximum length scale in the Solid phase (MaxSolid). MinSolid and MinVoid mean that the size of solid parts and cavities must be greater than the size of a prescribed circle or sphere

A non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-element solution of large-scale time-harmonic wave problems. It is well-known that the convergence rate of this kind of method strongly depends on the transmission condition enforced on the interfaces between the subdomains. Local conditions based on high-order absorbing boundary conditions (HABCs) have proved to