Narrow Results

This paper presents a combined numerical and experimental investigation into the vibroacoustic behavior of a traditional oud. An experimental modal analysis was conducted using impact hammer testing to determine the oud’s soundboard’s dynamic characteristics and frequency response function for up to 400 Hz. Finite element analysis was used to model the oud, incorporating its precise geometry, the wood’s orthotropic material properties, and its interaction with the surrounding air. Validation was performed by matching the numerical and experimental mode shapes and the natural frequencies. Harmonic acoustic analysis examined the oud’s sound pressure level radiation and cavity resonance. Structural–acoustic optimizations were conducted systematically, varying the soundhole’s size, the soundboard’s thickness, and the dimensions of the internal bracing to maximize the acoustics properties while minimizing the structural stress. The effects of these geometric factors on the instrument’s tonal characteristics were quantified. The results provide physical insights into the relationship between the oud’s construction and sound production. The methodology demonstrates a rigorous approach combining simulations and experimentation to comprehensively evaluate and optimize the vibroacoustic behavior of a musical instrument. This fundamental understanding could guide future improvements in the design of ouds.

This paper discusses two alternative formulations for developing orthotropic thick plate finite elements, namely the free formulation and the deviatoric strain formulation. These formulations are combined with interpolations for the transverse displacement and rotations that exactly satisfy the governing equations of Mindlin’s theory. Hence, the resulting element approximations are consistent for both thick and thin plates, and no locking occurs in the thin plate limit. The two formulations can be used to develop elements of arbitrary order and geometry, and several rectangular and triangular elements are derived in the paper. Examples are given in the paper to demonstrate the behavior and accuracy that is achieved with the proposed elements for both static and dynamics problems.

We present a general technique to solve one-dimensional time-dependent Schrödinger-type equations. A mapped infinite elements approach is used to eliminate spurious reflections of outgoing wave packets from the boundaries of the interval of interest. This procedure leads to more precise solutions because the space coordinates are discretized to approximate the solution in the entire physical domain. We show its utility giving numerical results on three typical examples: a bounded short-range potential; the unbounded potential of a particle in a dc field; and a Hamiltonian with an intrinsic time dependence like the Hamiltonian of a charged particle in an ac electromagnetic field.

The focus of this paper is on aligned fiber-reinforced composites, where fiber centers were randomly distributed in their cross-sections. The volume fractions of fibers were $V_f=30$% and $V_f=50$%. Samples were built with the help of the simulated annealing technique according to the chosen Radial Distribution Functions (RDFs). For each sample, the fields of local stresses and heat fluxes were simulated by finite element method. Then, homogenization by volume averaging was performed in order to investigate both the effective mechanical and thermal properties. The effect of RDF shape on elastic and thermal properties was quantified along with the influence of the probability of near neighbors of fibers on the physical properties. The more the fiber distributions deviate from Poisson’s Law, the higher the results compared to the lower bound of Hashin–Shtrikman.

For the solution of discretized ordinary or partial differential equations it is necessary to solve systems of equations with coefficient matrices of different sparsity pattern, depending on the discretization method; using the finite element method (FE) results in largely unstructured systems of equations. A frequently used iterative solver for systems of equations is the method of conjugate gradients (CG) with different preconditioners. On a multiprocessor system with distributed memory, in particular the data distribution and the communication scheme depending on the used data struture are of greatest importance for the efficient execution of this method. Here, a data distribution and a communication scheme are presented which are based on the analysis of the column indices of the non-zero matrix elements. The performance of the developed parallel CG-method was measured on the distributed-memory-system INTEL iPSC/860 of the Research Centre Jülich with systems of equations from FE-models. The parallel CG-algorithm has been shown to be well suited for both regular and irregular discretization meshes, i.e. for coefficient matrices of very different sparsity pattern.

Impact processes are often analyzed using the coefficient of restitution which represents the kinetic energy loss during impact. In this paper the effect of strain rate dependency of the yield stress on the coefficient of restitution is investigated experimentally and numerically for the impact of a steel sphere against a steel rod. Finite Element simulations using strain-rate dependent material behavior are carried out. In addition, Finite Element simulations with elastic-plastic material behavior, which ignore the strain rate dependency, are carried out as well as elastic material behavior. Comparisons between the experiments and the simulations using strain-rate dependent material behavior show good agreement, and also prove the strong dependency of the coefficient of restitution on the strain rate dependency of the yield stress for steel. The results from both, the experiments and the simulations show also the strong influence of the wave propagation in the rod on the coefficient of restitution.

This paper presents the development of a bidomain model of electrical defibrillation and post-shock arrhythmogenesis of the rabbit heart. The model incorporates a realistic representation of cardiac geometry, fiber structure, and membrane ionic processes. Fibrillation is induced in the rabbit heart with burst pacing. Defibrillation shocks of various strengths are delivered to the model in an attempt to terminate the arrhythmia. Two sets of defibrillation simulations are conducted based on the waveform of the defibrillation shock: monophasic and biphasic. The simulations presented here demonstrate the feasibility of modeling realistically the effect of the defibrillation shock on the heart.

A residual type a posteriori error estimator for finite elements is analyzed using a new technique. In this case, the error estimate is the result of two consecutive projections of the exact error on two finite-dimensional subspaces. The analysis introduced in this paper is based on a probabilistic approach, that is, the idea is to assess the average value of the effectivity index (the ratio estimated error over exact error) by assuming the randomness of the exact error. The average value characterizes the mean behavior of the estimator and it is found to be related with some geometric properties of the subspaces. These geometric properties are obtained from the standard matrices of the linear systems arising in the formulation of the finite element method.

In this work we propose a new numerical method for solving a thermomechanical coupled problem which arises as a mathematical model for the evolution of ice sheets profiles and the corresponding temperatures. From the accumulation–ablation ratio, the atmospheric temperature and the geothermic flux, the ice sheet profile is the solution of a moving boundary problem governed by a nonlinear convection–diffusion equation. Moreover, the mathematical model which governs the temperature distribution involves three nonlinearities: a reaction term due to the viscous dissipation, a Signorini boundary condition associated to the geothermic flux and an enthalpy term issued from the two-phase Stefan formulation of the polythermal regime. The problems are discretized in time with upwind characteristics schemes and in space with finite elements. The nonlinearities are solved either by fixed point methods or by duality techniques. Several numerical simulation examples involving real data sets issued from the Antartic ice sheet are shown.

We present a (somewhat) new finite element procedure for the analysis of higher Reynolds number fluid flows. While two-dimensional conditions and incompressible fluid flows are considered, the scheme can directly be used for three-dimensional conditions and also has good potential for compressible flow analysis. The procedure is based on the use of a nine-node element, optimal for incompressible analysis (the 9/3 or 9/4-c elements), and a Petrov–Galerkin formulation with exponential weight functions (test functions). These functions are established from the flow conditions along the edge- and mid-lines of the element. An important feature is that for low Reynolds number flow, the weight functions are the usual biquadratics and as higher Reynolds number flow is considered, the functions "automatically" skew so as to provide the necessary stability for the solution (the upwinding effect). Since the test functions are calculated by the flow conditions, no artificial constant is set by the analyst. The procedure is simple to implement. We present some solution experiences and conclude that while the procedure is not the "ideal" solution scheme sought, it has some valuable attributes and good potential for further improvements.

This paper deals with a posteriori error estimators for the linear finite element approximation of second-order elliptic eigenvalue problems in two or three dimensions. First, we give a simple proof of the equivalence, up to higher order terms, between the error and a residual type error estimator. Second, we prove that the volumetric part of the residual is dominated by a constant times the edge or face residuals, again up to higher order terms. This result was not known for eigenvalue problems.

In this paper we present a new approach in the study of Aorto–Coronaric bypass anastomoses configurations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary. The aim is to provide design indications in the perspective of future development for prosthetic bypasses. With a reduced model based on Stokes equations and a vorticity functional in the down field zone of bypass, a Taylor-like patch is found. A feedback procedure with Navier–Stokes fluid model is proposed based on the analysis of wall shear stress and its related indexes such as OSI.

In this paper we propose a general methodology to solve partial differential inequalities arising in the valuation of financial derivatives. Firstly we show how to build up a weak formulation and how to discretize it by implicit finite difference schemes in time and finite elements in space and we propose an iterative algorithm to solve the discrete variational inequality. Although the methodology is quite general, here it is applied to solve two important two-factor models: one for valuation of dividend paying Amerasian options and another for convertible bonds with stochastic interest rate and call and put features. In both cases we validate our results with some others existing in the literature.

In this work, a parallel three-dimensional solver for numerical simulations in computational electrocardiology is introduced and studied. The solver is based on the anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic reaction–diffusion equations describing the intra and extracellular potentials of the myocardial tissue. This model includes intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. The solver also includes the simpler anisotropic Monodomain model, consisting of only one reaction–diffusion equation. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations that can vary from the simple FitzHugh–Nagumo (FHN) model to the more complex phase-I Luo–Rudy model (LR1). The solver employs structured isoparametric Q₁ finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library. Large-scale computations with up to O(10⁷) unknowns have been run on parallel computers, simulating excitation and repolarization phenomena in three-dimensional domains.

We consider a new stabilized finite element method for advection-diffusion equations, where the Dirichlet boundary condition is imposed in a weak sense by Lagrange multipliers. The inf–sup condition of the corresponding mixed problem is circumvented by adding some further terms. Using the SUPG-stabilization, an optimal a priori estimate is shown for the singularly perturbed case. Then we present an a posteriori error estimator for our stabilized scheme. Some numerical experiments support the theoretical results. The present results are basic for a nonconforming three-field formulation of the problem.

We describe all operators on scalar finite element spaces which appear as the restriction of a second-order (linear) differential operator. More precisely we provide a family of isomorphisms between this space of discrete differential operators and products of some exotic finite element spaces. This provides a unified framework for the Regge calculus of numerical relativity and the Nédélec edge elements of computational electromagnetism.

The aim of this paper is to show that, for a linear second-order hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise affine finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a priori and a posteriori error estimates which admit, as much as it is possible, the decoupling of the errors committed in the temporal and spatial discretizations.

We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed by Dal Maso, Francfort and Toader,¹⁴ which takes into account body forces and surface loads. We employ adaptive triangulations and prove convergence results for the total, elastic and surface energies. In the case in which the elastic energy is strictly convex, we also prove a convergence result for the deformations.

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of this problem which combines Fourier truncation and finite element methods applied to each of the two-dimensional systems. We give the detailed a priori and a posteriori analyses of the discretization and present some numerical experiments which are in good agreement with the analysis.

In this paper we propose a new space and time finite elements discretization of the Landau–Lifshitz equations which may be readily used for numerical computations. We then prove its convergence to a weak solution in the sense given by Alouges and Soyeur or Labbé in the literature.