International Journal for Numerical Methods in Engineering最新文献

Wave propagation effects such as resonance and interference effects complicate the design of many acoustic devices, particularly when the dimensions of the device are in the order of the operating wavelength. At the same time, these complications also offer an opportunity for numerical optimization schemes to outperform designs achieved using traditional methodology. An example of a device sensitive to resonance and interference effects is the compression driver, the standard sound source for midrange acoustic horns in public address systems. Although ingenious and rather simple design guidelines have been developed, these unfortunately only apply to particular conceptual compression driver layouts. Here, we address a configuration for which no simple rules exist and apply numerical shape optimization for the design task. We employ a level-set geometry description of the crucial part of the compression driver interior. To avoid mesh changes when the level-set function is updated by a gradient-based optimization algorithm, we rely on the cut finite element (CutFEM) technique for the acoustic modeling. A particular modeling challenge here is that viscothermal losses cannot be ignored, due to narrow chambers and slits in the device. Up to quite recently, the modeling of such losses has required computationally expensive solutions of the linearized, compressible Navier–Stokes equations, making the use of shape optimization extremely challenging. Fortunately, a recently developed, accurate, but computationally inexpensive boundary-layer model is applicable in this case. For the first time in the context of a CutFEM/level-set method, the shape calculus needed to compute derivatives for the optimization algorithm is carried out in the fully discrete case, taking into account the discontinuities along the design boundary of the pressure derivatives and the normal field. Applying these techniques, the algorithm was able to successfully design the interior of a compression driver so that the final frequency response very closely matches an ideal response, derived by a lumped circuit model where wave interference effects are not accounted for.

This study introduces a framework for learning a low-depth surrogate quantum circuit (SQC) that approximates the nonlinear, dissipative, and hence non-unitary Bhatnagar–Gross–Krook (BGK) collision operator in the lattice Boltzmann method (LBM) for the $��{�D�}_{�2�}�{�Q�}_{�9�}�$ lattice. By appropriately selecting the quantum state encoding, circuit architecture, and measurement protocol, non-unitary dynamics emerge naturally within the physical population space. This approach removes the need for probabilistic algorithms relying on ancilla qubits and post-selection to reproduce dissipation, or for multiple state copies to capture nonlinearity. The SQC is designed to preserve key physical properties of the BGK operator, including mass conservation, scale equivariance, and $��{�D�}_{�8�}�$ equivariance, while momentum conservation is encouraged through penalization in the training loss. When compiled to the IBM Heron quantum processor's native gate set, assuming all-to-all qubit connectivity, the circuit requires only 724 native gates and operates locally on the velocity register, making it independent of the lattice size. The learned SQC is validated on two benchmark cases, the Taylor–Green vortex decay and the lid-driven cavity, showing accurate reproduction of vortex decay and flow recirculation. While integration of the SQC into a quantum LBM framework presently requires measurement and re-initialization at each timestep, the necessary steps towards a measurement-free formulation are outlined.

We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The optimization is performed over primal fields that satisfy the physical conservation law and the geometrical compatibility. We consider a reaction term in the conservation law, which has the effect of coupling all the optimality conditions. We first establish the well-posedness in the continuous setting. Then, we propose stable finite element discretizations that consistently approximate the continuous formulation, preserving its saddle-point structure and allowing for equal-order interpolation of all fields. Finally, we demonstrate the effectiveness of the proposed methods through a set of numerical examples.

This work presents a novel framework for enforcing minimum length-scale constraints in topology optimization, a fundamental challenge for ensuring manufacturable designs. Two complementary methodologies are proposed. The first, and primary, approach is based on local perimeter control, which regulates the amount of perimeter within localized regions of the design domain. Although the geometric interpretation may not be immediately intuitive, the formulation remains purely geometric and can be implemented by repeating standard filtering operations for a contour-related variable. The second methodology introduces a differentiable skeleton representation of the structure. Building upon recent advances in skeleton-based techniques, this approach avoids the definition of an auxiliary problem and instead leverages conventional filtering and projection tools widely used in topology optimization. Together, these two methodologies provide robust and computationally efficient mechanisms for imposing minimum member size constraints while maintaining consistency with the optimization framework. Their effectiveness is demonstrated through numerical experiments in linear elasticity and heat conduction, which highlight the robustness of the proposed methods across varying mesh densities and design complexities.

In this paper, we propose a novel multiphase approach for identifying input parameters in dynamic fracture propagation. Often, such parameters are partially known and uncertain with incomplete input data, resulting in challenges in predicting a reliable dynamic failure response. To address this, we employ a stochastic Bayesian inverse method to estimate input parameters in three distinct phases of a fracture model. As a case study, we analyze a virtual version of Kalthoff's dynamic fracture propagation test using a finite element model enhanced with embedded strong discontinuities, where cracks propagate in a mixed-mode manner, to demonstrate the effectiveness and robustness of the proposed method. The approach successfully identifies six material parameters, including the bulk modulus, shear modulus, tensile strength, shear strength, and the modes I and II fracture energies. Through different time intervals and measurements in each phase, our results show that the computed posterior mean values are closely aligned with the true parameters of the material, validating the reliability and accuracy of the method.

The probabilistic surrogates used by Bayesian optimizers make them popular methods when function evaluations are noisy or expensive to evaluate. While Bayesian optimizers are traditionally used for global optimization, their benefits are also valuable for local optimization. In this paper, a framework for gradient-enhanced unconstrained local Bayesian optimization is presented. It involves selecting a subset of the evaluation points to construct the surrogate and using a probabilistic trust region for the minimization of the acquisition function. The Bayesian optimizer is compared to conjugate-gradient and quasi-Newton optimizers from MATLAB and SciPy for unimodal problems with 2 to 40 dimensions. The Bayesian optimizer converges the optimality as deeply as the optimizers used for comparison and often does so using significantly fewer function evaluations. For the minimization of the 40-dimensional Rosenbrock function for example, the Bayesian optimizer requires half as many function evaluations as the MATLAB and SciPy optimizers to reduce the optimality by 10 orders of magnitude. For test cases with noisy gradients, the probabilistic surrogate of the Bayesian optimizer enables it to converge the optimality several additional orders of magnitude relative to the conjugate-gradient and quasi-Newton optimizers. The final test case involves the chaotic Lorenz 63 model and inaccurate gradients. For this problem, the Bayesian optimizer achieves a lower final objective evaluation than the SciPy quasi-Newton optimizer for all initial starting solutions. The results demonstrate that a Bayesian optimizer can be competitive with quasi-Newton and conjugate-gradient optimizers when accurate gradients are available, and significantly outperforms them when the gradients are inaccurate.