Mesh Size Research Articles

A Spectral Element Solution of the Poisson Equation with Shifted Boundary Polynomial Corrections: Influence of the Surrogate to True Boundary Mapping and an Asymptotically Preserving Robin Formulation

Abstract We present a new high-order spectral element solution to the two-dimensional scalar Poisson equation subject to a general Robin boundary condition. The solution is based on a simplified version of the shifted boundary method employing a continuous arbitrary order hp-Galerkin spectral element method as the numerical discretization procedure. The simplification relies on a polynomial correction to avoid explicitly evaluating high-order partial derivatives from the Taylor series, which traditionally is used within the shifted boundary method. Here, we apply an extrapolation and novel interpolation approach to project the basis functions from the true domain onto the approximate surrogate domain. The solution provides a method that naturally incorporates curved geometrical features of the domain, overcomes complex and cumbersome mesh generation, and avoids problems with small cut cells. Dirichlet, Neumann, and Robin boundary conditions are enforced weakly through a generalized: (i) Nitsche’s method and (ii) Aubin’s method. A consistent asymptotic preserving formulation of the embedded Robin formulations is presented. Several experiments and analyses of the numerical properties of the various weak forms are showcased. We include convergence studies under polynomial increase of the basis functions, p, mesh refinement, h, and matrix conditioning to highlight the spectral and algebraic convergence features, respectively. With this, we assess the influence of errors across variational forms, polynomial order, mesh size, and mappings between the true and surrogate boundaries.

Nodal auxiliary space preconditioners for mixed virtual element methods

We propose nodal auxiliary space preconditioners for facet and edge virtual elements of lowest order by deriving discrete regular decompositions on polytopal grids and generalizing the Hiptmair-Xu preconditioner to the virtual element framework. The preconditioner consists of solving a sequence of elliptic problems on the nodal virtual element space, combined with appropriate smoother steps. Under assumed regularity of the mesh, the preconditioned system is proven to have bounded spectral condition number independent of the mesh size and this is verified by numerical experiments on a sequence of polygonal meshes. Moreover, we observe numerically that the preconditioner is robust on meshes containing elements with high aspect ratios.

Finite element based micromagnetic simulations of heterogeneous magnetic microstructures

AbstractMagnetic materials play a crucial role in our everyday lives. As permanent magnets, they are core components in electric motors such as generators for wind turbines, or, as magnetocaloric magnets, they have the potential to change the cooling technology of tomorrow. All of this makes these materials key contributors to “green” energy conversion technology. Accordingly, pushing the development of these materials with a special focus on the performance, efficiency, and harmlessness of the material components contained for humans and the environment is of crucial importance. This work deals with the finite element‐based simulations within the framework of the micromagnetic theory to numerically support the quest of characterizing novel magnetic materials. The main focus remains on the numerical modeling of permanent magnetic polycrystalline materials and the influence of grain boundaries on the effective magnetization. For this purpose, large‐scale simulations of permanent magnetic neodymium‐iron‐boron () samples are carried out and the influence of different mesh sizes on the effective magnetization behavior is investigated.

Superconvergence analysis of a low order expanded conforming mixed finite element method for the extended Fisher–Kolmogorov equation

This paper is devoted to the superconvergence analysis of a low order expanded conforming mixed finite element method(MFEM) for the extended Fisher–Kolmogorov equation. Both semi-discrete and linearized backward Euler fully-discrete schemes are analyzed with bilinear and Nédéleć elements. The present work has two main contributions: One is that some a priori bounds of the approximations are derived, which lead to the unique solvability of the semi-discrete scheme and make the nonlinear term can be dealt with efficiently. By such a way, the superclose properties and superconvergence results can be derived through the high accuracy results of the above two elements and the interpolated postprocessing technique, respectively. The other one is that a novel splitting technique is utilized to deal with the nonlinear term, which can avoid the use of popular error splitting technique and the restrictions between the time step size and mesh size. Besides, the combination technique of interpolation and projection operators also plays an important role in the superclose and superconvergence analysis. Finally, some numerical results are provided to show the validity of the theoretical analysis.

Bayesian mesh optimization for graph neural networks to enhance engineering performance prediction

Abstract In engineering design, surrogate models are widely employed to reduce the computational costs of simulations by approximating design variables and geometric parameters from computer-aided design (CAD) models. However, traditional surrogate models often lose critical information when simplified to lower dimensions, and face challenges in handling the complexity of 3D shapes, especially in industrial datasets. To address these limitations, we propose a Bayesian graph neural network (GNN) framework that directly learns geometric features from CAD mesh representations for accurate engineering performance prediction. Our framework leverages Bayesian optimization (BO) to dynamically determine the optimal mesh element size, significantly improving model accuracy while balancing computational efficiency. This approach addresses the challenge of mesh quality by optimizing mesh resolution, ensuring that critical geometric features are preserved in 3D deep-learning-based surrogate models. Unlike existing models that rely on static or predefined mesh resolutions, our method adapts mesh size based on the task, making it highly flexible for a wide range of engineering applications. Experimental results demonstrate that mesh quality directly impacts prediction accuracy, and the proposed BO-EI GNN model outperforms state-of-the-art models such as 3D CNN, SubdivNet, GCN, and GNN in predicting mass, rim stiffness, and disk stiffness. Our method also significantly reduces the computational costs compared to traditional optimization techniques. The proposed framework shows promising potential for application in finite element analysis (FEA) and other mesh-based simulations, enhancing the utility of surrogate models across various engineering fields.

Formulation, E-Beam Crosslinking, and Comprehensive Characterisation of Lavender Oil-Enriched Hydrogels

This study focused on the formulation, electron beam (e-beam) crosslinking, and characterisation of hydrogels enriched with lavender oil (LO) to enhance their structural and functional properties for biomedical applications. Stable hydrogels were synthesised using water-soluble polymers and suitable ratios of Tween 80 and Isopropyl alcohol (IPA) as surfactant and co-surfactant, respectively, via e-beam irradiation at doses up to 70 kGy. The most effective crosslinking was achieved with a radiation dose of 30 kGy, depending on the concentrations of surfactants and LO. LO-enriched hydrogels exhibited enhanced superabsorbent swelling (7700% to 18,000%) and faster equilibrium rates than the control hydrogel. Structural analysis revealed a flexible spongiform porous architecture with larger mesh sizes (156 nm to 246 nm) and adequate elastic moduli (130 to 308 Pa). Degradation tests aligned with swelling data, demonstrating a degradation rate of 12% after 35 days, indicating an appropriate balance of stability and degradation. These findings suggest that e-beam technology, in conjunction with LO and surfactant addition, can effectively tailor hydrogel properties for biomedical applications, making them promising candidates for further research in wound care, drug delivery systems, and other biological applications.

Process optimization and finite element modeling in magnetorheological abrasive finishing of SS-316L with surface characterization

This study explores the potential of Magnetorheological Abrasive Finishing (MRAF) for ultra-precision finishing of SS-316L using a high-performance Nd-Fe-B (N-35 grade) magnetic tool. Key parameters, including the relationship between normal force (Fn) and working gap, magnetic flux distribution, and finishing spot area, were analyzed using ANSYS 2020 R1® Magnetostatic module simulations. Material removal rate (MRR) and surface roughness (Ra) were optimized through response surface methodology (RSM) using a central composite design (CCD) with two primary input factors: SiC abrasive volume fraction (5%, 10%, 15%) and abrasive mesh size (800, 1000, 1200). Statistical analysis via ANOVA revealed a significant influence of process variables, achieving a remarkable surface finish with a minimum Ra of 52 nm in just 60 min, utilizing an MR fluid with 10% SiC abrasives. Microscopic and spectroscopic evaluations confirmed enhanced surface morphology and microstructural refinement. Moreover, bioactivity studies in simulated body fluid highlighted improved hydroxyapatite layer formation on the finished SS-316L samples, underscoring the process’s potential for biomedical applications.

Variational evolution of discrete one-dimensional second-order functionals

A variational scheme of evolution (minimizing movements) is applied to a sequence of discrete functionals converging, as the mesh size tends to zero, to the prototypical second-order functional with free-discontinuities. At fixed mesh size, a discrete evolution can be defined, depending on a (small) time parameter. We study the limit problem when both the mesh size and the time step tend to zero. The method provides a function which matches the expected evolution of the free-discontinuity limit functional. From a mechanical point of view, the model can be interpreted as the evolution from a non-equilibrium state, of a rod with possible crease discontinuities and fracture.

Classification of the Penguluran River and Mbambang River using Macroinvertebrate with TWINSPAN Analysis

The Penguluran River and Mbambang River are strategic rivers from an ecological, economic, and social perspective. In the last 5 years there have been flood disasters which can affect the communities within them, for example macroinvertebrates. The aim of the research is the classification of macroinvertebrate habitat groups in Penguluran River and Mbambang River. Research methods uses survey methods and secondary macroinvertebrate data in 2023. Sampling at 25 sites based on different land uses by kicking technique with a hand net (mesh size of 500 μm) in a 10 meter long riffle area. Data analysis using TWINSPAN (Two-way Indicator Species Analysis). TWINSPAN analysis obtained 9 site of group from 25 observation sites (site of groups A–I). Furthermore, the 9 site groups were divided into 3 large groups based on the level of macroinvertebrate sensitivity. Site of group E and F in Argotirto Village and Sumberagung Village have light sensitivity (30%) higher than medium sensitivity (20%) with current vellocity ranges medium to fast, rock and gravel substrates that experience light smoothering, plantation land use (coffee, mangosteen, and cloves) showed light degradation. Site of group A, B, C, H, and I in Argotirto Village, Sumberagung Village, and Sidodadi Village have moderate sensitivity (30%) higher than light sensitivity (20%), current velocity ranges slow to fast, rock substrate and gravel that experienced moderate smoothering, secondary forest land use, plantations (sugar cane, coffee, banana), settlements, and livestock showed moderate degradation. Site of group D and E in Argotirto Village and Sumberagung Village have tolerant sensitivity (36%) than sensitive macroinvertebrates (28%), current velocity ranges medium to fast, rock and mud substrates that experience heavy smoothering, plantation land use (coconut , banana, clove and mangosteen) showed heavy degradation. TWINSPAN analysis of 9 site of group shows light degradation, moderate degradation, and heavy degradation.

Local discontinuous Galerkin methods with implicit–explicit BDF time marching for Newell–Whitehead–Segel equations

The Newell–Whitehead–Segel type equations with time-dependent Dirichlet boundary conditions are solved by the local discontinuous Galerkin (LDG) method coupled with the implicit–explicit backward difference formulas (IMEX-BDF). With a suitable setting of numerical fluxes and by the aid of the multiplier technique and the a priori error assumption technique, the optimal error estimate for the corresponding fully discrete LDG-IMEX-BDF schemes is obtained by energy analysis, under the condition τ ≤ C h 1 / s , where h and τ are mesh size and time step, respectively, the positive constant C is independent of h, and s = 1 , … , 5 is the order of the IMEX-BDF method. Numerical experiments are also presented to verify the accuracy of the considered schemes.

The Effect of Season and The Implications For Sustainable Fisheries on The Catch Results of Yellowfin Tuna In Indonesia

This study assessed the purse seine, handline and pole and line catches at PPS (Samudera Fishing Port Kendari) specifically targeting skipjack and yellowfin tuna in the Banda Sea. Although there has been a rise in tuna output over the past two years, the examination of fish size in September until November revealed substantial fluctuation. Additionally, the implementation of the moratorium policy had a detrimental effect. Ensuring the sustainability of fisheries in the Banda Sea, particularly for large pelagic fish like skipjack and yellowfin tuna, necessitates the implementation of adaptive management and selective fishing practices, with a particular focus on enforcing mesh size regulations. The aims of this study were to examine the patterns of tuna fisheries landing at PPS, specifically focusing on the sorts of catches made using purse seine, handline, and pole and line fishing methods. Additionally, the study aimed to assess the length frequency distribution of Thunnus albacares caught using purse seine, handline, and pole and line fishing gear. The methodology offers a thorough framework for eval_uating the sustainability of Thunnus albacares fisheries in PPS Kendari. Policymakers can develop effective management plans for long-term resource sustainability by assessing catch composition, productivity, and size distribution across various fishing gears. The analysis of this study conducted in September - November 2023 revealed that the fish catches varied in size, ranging from 13 cmFL to 124 cmFL.

Analysis of fluid forces impacting on the impeller of a mixed flow blood pump with computational fluid dynamics.

This study presents four different impeller designs to compare hydrodynamic forces. Numerical simulation studies are performed via computational fluid dynamics to specify and investigate the hydraulic forces impacting the impeller of the mixed-flow blood pump with a volute. The design point of this pump is that the flow rate is 5 L/min, the rotational speed is 8000 rpm, and the manometric head is 100 mmHg. The designed impellers are placed in the same volute and simulation studies are performed with the same mesh size (17.3 million cells) of the pumps. The simulation studies have been conducted in setting 1050 kg/m3 blood density, 35 cP fluid viscosity, and SST-kω turbulence model. Additionally, this study examines the changes in hydraulic forces and hydraulic efficiency with fluid viscosity. As a result of experimental simulation studies, the highest hydraulic efficiencies of 40.87% and 39.5% are achieved in the case of the shaftless-grooveless and shafted-grooveless impeller, respectively. The maximum axial forces are obtained from the pump with the shaftless-grooveless impeller. Whereas radial forces, maximum values are calculated in the pump with the shaftless-outer groove impeller for all flow rates. Finally, the wall shear stresses, which are important for blood pump designs, are evaluated and the maximum value of 227 Pa is observed in the pump impeller with a shaftless-grooved.

Numerical analysis of axially loaded concrete-filled steel tubular columns strengthened with CFRP grid-reinforced ECC

Carbon fiber-reinforced polymer (CFRP) and engineered cementitious composites (ECC) are commonly used to reinforce structural elements, with proven effectiveness in enhancing the performance of concrete-filled steel tube (CFST) columns as shown in prior experimental studies. However, the complex interaction among the components of the reinforced columns, including CFRP, ECC, the steel tube, and the concrete core, as well as the underlying mechanical mechanisms, remain insufficiently understood. This research aims to fill these gaps by developing a 3D finite element (FE) model of circular CFST short columns reinforced with CFRP grid-reinforced ECC for comprehensive numerical analysis. Sensitivity analyses are conducted to determine the governing parameters in the numerical simulation, including mesh size and critical plasticity parameters for the concrete damage model, such as the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian (Kc), and the dilation angle (ψ) for both the concrete core and ECC. The model also accounts for the effects of concrete confinement provided by the CFRP grid-reinforced ECC layer and the circular steel tube. The accuracy of the FE model is validated against existing experimental data, and the model is subsequently used to investigate the behavior of reinforced CFST columns under varying geometric and material properties. The study examines failure modes, axial load-displacement responses, stress distributions, and the contribution of each material component to the load-bearing capacity of the strengthened columns. The results indicate an increase in ultimate axial strength ranging from 13% to 20% for the reinforced CFST columns. While the compressive strength of the ECC has a moderate effect on axial resistance, increasing ECC thickness, concrete strength, and steel tube yield strength significantly enhances the columns’ load-bearing capacity. Finally, a novel design model is proposed and validated, which accounts for the confinement effects provided by the CFRP grid and ECC on the concrete core.

Capillary Skimming of Floating Microplastics via a Water-Bridged Ratchet.

Floating microplastics (MPs) have recently become a major concern in marine pollution; however, current filter-based technology is hardly effective for directly removing such MPs from the water surface because of specific mesh size and clogging issues. This paper introduces a new skimming concept for removing floating MPs utilizing capillary force mediated by the elevation of a hydrophilic ratchet at the air-water interface. MPs floating near the ratchet surface are spontaneously forced toward the ratchet with a concave water meniscus, driven by the Cheerios effect. The MPs can then be skimmed and temporarily held by the deforming concave water meniscus as the ratchet rises. Here, it is found that the stability of the water bridge plays a crucial role in skimming success because it provides capillary adhesion between the MP and the ratchet. The proposed capillary skimming method is observed to be effective across nearly all types of floating MPs, ranging in size from 1 to 4 mm, and with densities varying from 0.02 to 0.97 gcm- 3, which is also demonstrated by a prototype of marine robot cleaner.

Potential of the upcoming Biomass P-band radar mission for digital terrain modelling beneath dense tropical forests: first accuracy assessment

Abstract. P-band radar surveys can be used to produce digital elevation models (DEMs) at ground level in dense tropical forest areas. However, the previous performance studies were carried out on DEMs derived from high-resolution synthetic aperture radar (SAR) acquisitions, while the upcoming Biomass space mission should provide DEMs at a coarser resolution due to a frequency bandwidth of 6 MHz in range. The aim of this study is to predict the quality of the DEM products derived from Biomass data through dense forest. A DEM was produced in a slant range geometry at a 15-m mesh size using SAR tomography. It was compared to the reference LiDAR survey in terms of elevation and slope, and the statistical distribution of the corresponding error was analysed with regards to the radar off-nadir angle and to the local slope and aspect. The results show that the DEM elevation has no systematic error despite the presence of forest, and it has an RMS error of 3 meters. The DEM slope has a mean error of 2° and an RMS error of 6°. The behaviour of these errors for different terrain slopes and aspects will allow to predict the quality of Biomass DEMs on a variety of terrestrial landscapes.

Distribution, sorption patterns, and outflows of riverine microplastics-affiliated linear alkylbenzenes and polycyclic aromatic hydrocarbons in a dynamic coastal zone.

Microplastics (MPs) pollution has emerged as a global concern. To mitigate the potential threats by MPs, particularly to coastal regions, it is crucial to comprehend the environmental behavior of MPs and their affiliated chemicals. In the present study, we collected floating MPs using a Manta net (0.33 mm mesh size) in a one-year sampling event in 2022 from the eight major estuaries in the Pearl River Delta, China, and also from five coastal sites in August and December in the same year. Nineteen linear alkylbenzenes (∑19LAB) and 16 polycyclic aromatic hydrocarbons (∑16PAH) affiliated with MPs were measured. The mean concentrations of MPs-affiliated ∑19LAB and ∑16PAH were 6710 (range: 3400-12300) and 5310 (range: 817-19,600) ng g-1, respectively, at the estuarine sites, and were 4920 (range: 2400-7600) and 2610 (range: 911-7890) ng g-1, respectively, at the coastal sites. Significant correlations were found between logarithmic MPs-water partition coefficients (log Kpw) and logarithmic suspended particulate matter-water partition coefficients (log Kd) values for LABs and PAHs, indicating analogous partitioning dynamics for MPs and suspended particulate matter with water. The annual riverine outflows were 1170 and 414 g for ∑19LAB and ∑16PAH, respectively. Although the riverine outflows of LABs and PAHs carried by MPs remain negligible compared to those by suspended particulate matter, an upward trend was identified between 2018 and 2022. Notably, the riverine input of LABs and PAHs carried by suspended particulate matter to the coastal ocean decreased from 2005/2006 to 2022, due to a combination of improved technological processes and energy structures.

An analysis of discontinuous Galerkin method for Electrical Impedance Tomography with partial data

In this work, we extend our previous work (Li and Wang, 2023) of the discontinuous Galerkin (DG) method for Electrical Impedance Tomography (EIT) with full data to partial data where the current and voltage measurements are taken only on part of the boundary. Additionally, we provide the convergence analysis of the DG approximation for EIT for partial data based on an iterative method with Tikhonov regularization. We prove that the minimizers of the discrete optimization problems converge to a minimizer of the continuous optimization problem as the mesh sizes of the discretization approach zero. Numerical results for the recovery of conductivities are tested with different types of partial data. The partial data results are demonstrated to be comparable to the full data results.

Experimental research on nonlinear vibration characteristics of double-layer mining string for deep-sea hydrate extraction under internal and external flow excitation

The vibration mechanism of the deep-sea hydrate mining string is extremely complex due to the combined effects of internal gas–liquid solid multiphase flow, structural contact collision, soil creep effect, and external ocean random load. Based on this, using the principle of similarity, a simulation experimental platform for the vibration of double-layer mining riser in deep-sea hydrate wells under internal and external flow excitation is developed, considering the vortex-induced effect of external flow field on the mining riser in the ocean section (which can simulate a maximum ocean flow velocity of 0.5 m/s), the three-phase flow-induced effect of gas–liquid–solid inside (which can simulate a maximum flow velocity of 2.0 m/s), and the coupling effect of mining string–conductor anchor node (CAN)–seabed. The influence of particle size, phase ratio, three-phase flow, and external flow velocity on the vibration response characteristics and nonlinear behavior of mining string are investigated. It is found that the vibration of vertical string is significantly affected by external ocean currents and internal three-phase currents. The vibration displacement amplitude of the horizontal section (average 0.08 mm) is significantly smaller than those of the vertical section (average 70 mm). The strong vibration positions of the vertical and horizontal sections of the mining string are different, in that the vertical section is mostly located below the middle section (just at 1800–2400 mm), while the horizontal section is mostly located at the three-phase inlet (just at 500 mm). The vertical section of the mining string presents a motion trajectory of oblique straight line, wide oblique straight line, or approximately wide oblique straight line, while the horizontal section is mostly a chaotic trajectory or an “8”-shaped chaotic trajectory. The decrease in particle mesh size and the increase in solid-phase proportion are reflected in the difficulty and accumulation of particle transport, leading to an increase in vibration displacement, as well as a decrease in vibration displacement amplitude and vibration energy. When the particle size set as 50 mesh, the displacement of mining string is largest, just for 110 mm of vertical section and 0.08 mm of horizontal section. The increase in the proportion of gas phase will lead to changes in the flow state of multiphase flow, which will affect the vibration displacement amplitude of the mining string to varying degrees. The increase in three-phase flow velocity further induces vibration of the mining string, and when the flow velocity is between 1.5 and 1.75 m/s, it will resonate with the string system, resulting in a sudden increase in the amplitude of vibration displacement. The research results can effectively guide operations and improve the service life of deep-sea hydrate mining riser.

The solution of sound propagation modeling problems for environment impact assessment by the mode parabolic equations methoda).

The method of sound propagation modeling based on the mode parabolic equations (MPEs) theory is applied to the verification scenarios for environmental impact assessment. The results for selected scenarios from the 2022 Cambridge Joint Industry Programme Acoustic Modelling Workshop and the configuration of the computational programs AMPLE and MPE for these scenarios is discussed. Furthermore, it is revealed how the results for these scenarios change in the case of the bottom slope across and along the propagation path. It is observed that for the cross-slope propagation scenario, the distribution of acoustic energy over decidecade frequency bands does not depend on the slope angle and is practically the same as that for range-independent environment. At the same time, the dependence of energy distribution is noticeable for up- and downslope propagation scenarios, where greater slope angles result in higher propagation loss. It is also shown that MPEs are capable of adequately handling typical sound propagation problems related to the environmental impact assessment for frequencies up to 1000 Hz. A possibility of using frequency-dependent mesh size and number of modes must be implemented in codes based on this approach.

Utilizing T-Line Mesh for Periumbilical Hernia Repair: Evaluation of Short-term Outcomes.

Abdominal periumbilical hernias are prevalent within the adult population. When symptomatic, quality of life may be affected. This case series of 10 patients evaluates the short-term outcomes of using the T-Line mesh in periumbilical hernia repair. A retrospective review of adult patients with symptomatic periumbilical abdominal hernia treated with open repair with T-Line mesh was performed at a tertiary referral center. Ten patients with an average age of 51 years were offered surgical treatment. Measures of postoperative outcomes included readmission within the 30-day postoperative period; recurrence; surgical site infection; development of seroma and hematoma; and the presence of pain, numbness, or bloating. Descriptive statistics were computed in Microsoft Excel. All 10 patients reported improvement in symptoms. All repairs were elective and classified as clean (100%). Hernias included 40% primary umbilical, 50% ventral, and 10% incisional. The average defect size was 10 cm2, with a range from 1 to 25 cm2. The T-Line mesh was placed in a sublay manner, with an average mesh size of 36 cm2. No patients were readmitted in the 30-day postoperative period. There were no occurrences of surgical site infection or hernia recurrence. No hospital readmissions and no follow-up visits with hernia recurrence were noted at 3 months. We present a case series of 10 patients presenting with symptomatic periumbilical hernias who underwent repair with the T-Line hernia mesh without short-term surgical occurrences. Long-term studies are required to accurately reflect safety and efficacy.