Engineering with Computers最新文献

Forecasting tumor progression and assessing the uncertainty of predictions play a crucial role in clinical settings, especially for determining disease outlook and making informed decisions about treatment approaches. In this work, we propose TGM-ONets, a deep neural operator learning (PI-DeepONet) based computational framework, which combines bioimaging and tumor growth modeling (TGM) for enhanced prediction of tumor growth. Deep neural operators have recently emerged as a powerful tool for learning the solution maps between the function spaces, and they have demonstrated their generalization capability in making predictions based on unseen input instances once trained. Incorporating the physics laws into the loss function of the deep neural operator can significantly reduce the amount of the training data. The novelties of the design of TGM-ONets include the employment of a convolutional block attention module (CBAM) and a gating mechanism (i.e., mixture of experts (MoE)) to extract the features of the input images. Our results show that the TGM-ONets not only can capture the detailed morphological characteristics of the mild and aggressive tumors within and outside the training domain but also can be used to predict the long-term dynamics of both mild and aggressive tumor growth for up to 6 months with a maximum error of less than 6.7 (times 10^{-2}) for unseen input instances with two or three snapshots added. We also systematically study the effects of the number of training snapshots and noisy data on the performance of TGM-ONets as well as quantify the uncertainty of the model predictions. We demonstrate the efficiency and accuracy by comparing the performance of TGM-ONets with three state-of-the-art (SOTA) baseline models. In summary, we propose a new deep learning model capable of integrating the TGM and sequential observations of tumor morphology to improve the current approaches for predicting tumor growth and thus provide an advanced computational tool for patient-specific tumor prognosis.

This study introduces a novel dynamic infinite meshfree method, termed RK-DIMM (reproducing kernel dynamic infinite meshfree method), which is specifically developed for analyzing elastic half-spaces with cavities under the influence of both P-waves and SV-waves. RK-DIMM integrates the principles of reproducing kernel particle methods with dynamic infinite element techniques to enhance computational efficiency and accuracy in wave propagation simulations. The method partitions the infinite domain into near and far domains using artificial boundaries, utilizing RK in the near domain and DIMM in the far domain. Through the application of stabilized conforming nodal integration and naturally stabilized nodal integration, RK-DIMM achieves accurate and stable solutions. Our rigorous benchmark comparisons have confirmed the method’s exceptional ability to simulate wave dissipation and reflections with high accuracy and computational efficiency. RK-DIMM has proven to be highly effective in mimicking soil responses to synthetic earthquake forces, closely aligning with analytical predictions, and has demonstrated robust performance in scenarios involving underground cavities. Furthermore, its application to real earthquake data, particularly the 1999 Chi-Chi earthquake, underscores its practical utility and relevance. The results from this study highlight RK-DIMM’s potential as a transformative tool in computational geomechanics, significantly enhancing the precision and reliability of seismic impact assessments on civil infrastructures.

This work presents the first method for generating tetrahedral-based volume meshes dedicated to the NURBS-enhanced finite element method (NEFEM). Built upon the developed method of generating feature-independent surface meshes tailored for NEFEM, the proposed mesh generation scheme is able to grow volume elements that inherit the feature-independence by using the surface mesh as the initial boundary discretisation. Therefore, the generated tetrahedral elements may contain triangular faces that span across multiple NURBS surfaces whilst maintaining the exact boundary description. The proposed strategy completely eliminates the need for de-featuring complex watertight CAD models. At the same time, it eliminates the uncertainty originated from the simplification of CAD models adopted in industrial practice and the error introduced by traditional isoparametric mesh generators that produce polynomial approximations of the true boundary representation. Thanks to the capability of having element faces traversing multiple geometric surfaces, small geometric features in the CAD model no longer restrict the minimum element size, and the user-required mesh spacing in the generated mesh is better satisfied than in traditional meshes that require local refinement. To demonstrate the ability of the proposed approach, a variety of CAD geometries are meshed with the proposed strategy, including examples relevant to the fluid dynamics, wave propagation and solid mechanics communities.

An adaptive phase-field total Lagrangian material point method (APTLMPM) is proposed in this paper for effectively simulating the dynamic fracture of two-dimensional soft materials with finite deformation. In this method, the governing equations for the fracture of soft materials are derived by integrating the phase-field fracture model with the total Lagrangian material point method (TLMPM), and corresponding discrete equations are then formulated with explicit time integration. To address the significant computational issue in terms of memory and processing time, an adaptive technique for dynamically splitting particles and background grids in the phase-field TLMPM is proposed, based on the phase-field values of the particles. To further maintain continuity of the physical field throughout the computational process and consider the characteristics of the field update, an information remapping strategy is developed. Several representative numerical examples are presented to demonstrate the accuracy and efficiency of the proposed APTLMPM by comparing the simulation results with experimental data and those as obtained with other numerical methods.

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. Existing methods often fix boundary parameters, leading to challenges in elongated geometries such as fluid channels and tubular reactors. This paper presents an innovative solution for the boundary parameter matching problem, specifically designed for analysis-suitable parameterizations. We employ a sophisticated Schwarz–Christoffel mapping technique, which is instrumental in computing boundary correspondences. A refined boundary curve reparameterization process complements this. Our dual-strategy approach maintains the geometric exactness and continuity of input physical domains, overcoming limitations often encountered with the existing reparameterization techniques. By employing our proposed boundary parameter matching method, we show that even a simple linear interpolation approach can effectively construct a satisfactory analysis-suitable parameterization. Our methodology offers significant improvements over traditional practices, enabling the generation of analysis-suitable and geometrically precise models, which is crucial for ensuring accurate simulation results. Numerical experiments show the capacity of the proposed method to enhance the quality and reliability of isogeometric analysis workflows.

3D Traction Force Microscopy (3DTFM) constitutes a powerful methodology that enables the computation of realistic forces exerted by cells on the surrounding extracellular matrix (ECM). The ECM is characterized by its highly dynamic structure, which is constantly remodeled in order to regulate most basic cellular functions and processes. Certain pathological processes, such as cancer and metastasis, alter the way the ECM is remodeled. In particular, cancer cells are able to invade its surrounding tissue by the secretion of metalloproteinases that degrade the extracellular matrix to move and migrate towards different tissues, inducing ECM heterogeneity. Typically, 3DTFM studies neglect such heterogeneity and assume homogeneous ECM properties, which can lead to inaccuracies in traction reconstruction. Some studies have implemented ECM degradation models into 3DTFM, but the associated degradation maps are defined in an ad hoc manner. In this paper, we present a novel multiphysics approach to 3DTFM with evolving mechanical properties of the ECM. Our modeling considers a system of partial differential equations based on the mechanisms of activation of diffusive metalloproteinase MMP2 by membrane-bound metalloproteinase MT1-MMP. The obtained ECM density maps in an ECM-mimicking hydrogel are then used to compute the heterogeneous mechanical properties of the hydrogel through a multiscale approach. We perform forward and inverse TFM simulations both accounting for and omitting degradation, and results are compared to ground truth reference solutions in which degradation is considered. The main conclusions resulting from the study are: (i) the inverse methodology yields results that are significantly more accurate than those provided by the forward methodology; (ii) ignoring ECM degradation results in a considerable overestimation of tractions and non negligible errors in all analyzed cases.

We present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of deal.t (deal.II with T-splines) and main differences when using deal.t in contrast to deal.II. The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on deal.II, T-splines may be applied to various different PDEs.

This article presents a new algorithm designed to create a dynamic r-adaptive mesh within the framework of isogeometric analysis. The approach is based on the simultaneous computation of adaptive meshes using a nonlinear parabolic Monge–Ampere equation with a resolution of partial differential equations in multidimensional spaces. The technique ensures the absence of geometric boundary errors and is simple to implement, requiring the solution of only one Laplace scalar equation at each time step. It utilizes a fast diagonalization method that can be adapted to any dimension. Various numerical experiments were conducted to validate an original parabolic Monge–Ampere solver. The solver was respectively applied to Burgers, Allen–Cahn, and Cahn–Hilliard problems to demonstrate the efficiency of the new approach.

This study proposes a generalized nth-order perturbation method based on (isogeometric) boundary element methods for uncertainty analysis in 3D acoustic scattering problems. In this paper, for the first time, we derive nth-order Taylor expansions of 3D acoustic boundary integral equations, taking incident wave frequency as a random input variable. In addition, subdivision surface basis functions used in geometric modeling are employed to discretize the generalized nth-order derivative boundary integral equations, in order to avoid cumbersome meshing procedure and retain geometric accuracy. Moreover, the fast multipole method is introduced to accelerate the stochastic perturbation analysis with boundary element methods. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed uncertainty quantification algorithm.

We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These integral equations are discretized by Galerkin’s method, which especially enables the mathematically correct regularization of the hypersingular integral operator. In order to circumvent densely populated system matrices, we employ the isogeometric embedded fast multipole method, which is based on interpolation of the kernel function under consideration on the reference domain, rather than in space. To overcome the prohibitive cost of the potential evaluation in case of many evaluation points, we also accelerate the potential evaluation by a fast multipole method which interpolates in space. The result is a frequency stable algorithm that scales essentially linear in the number of degrees of freedom and potential points. Numerical experiments are performed which show the feasibility and the performance of the approach.