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DOE OSTI2023

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Surface smoothing for laser powder-bed Ti-6Al-4V by a transient liquid phase

Surface roughness is the primary driver of fatigue for additively manufactured metals. To address surface roughness, this work introduces a new method to smooth features beyond line-of-sight without material removal. The method applies a coating that triggers local surface remelting by activating a eutectic reaction during heat treatment. The associated liquid phase then wets and isothermally solidifies into a smoother surface. For Ti-6Al-4V fabricated with laser powder bed fusion, samples with and without TLP smoothing (using a Cu coating) were characterized with a suite of techniques, including mechanical testing, electron backscatter diffraction, synchrotron X-ray tomography, and fractography. TLP smoothing reduced surface roughness by 80% and amplified compressive residual stress at the surface by about 50%. With statistically equivalent virtual microstructures, crystal plasticity scrutinized the roles of phases, porosity, and surface roughness. Although the tensile strain-to-failure was reduced to 1% strain, the TLP smoothing process increased high-cycle fatigue strength by about 20% compared to control samples, pointing to future opportunities to optimize the new process through various coating compositions and heat treatment schedules. Overall, this work establishes a new paradigm for treating surfaces of materials for smoothness and compressive residual stress.

Additive manufacturing↗

DOE OSTI2020

Scalable line and plane relaxation in a parallel structured multigrid solver

The efficient solution of sparse, linear systems that arise through the discretization of partial differential equations remains a key challenge for a range of high performance scientific simulations. One approach for reducing data movement and improving performance is by exposing and exploiting structure in a problem through the use of robust structured multilevel solvers. By choosing coarsening that preserves the structure of the problem, these methods maintain efficient structured computation and communication throughout the multigrid hierarchy. However, when coarsening is not permitted to be dependent on the operator, anisotropy must be addressed by the smoother — producing error compatible for coarse-grid correction with structured coarsening. Here, the components required in a scalable parallel structured solver are described with a focus on memory and communication efficiency of robust smoothers. While the implementation of communication and memory reduction techniques in smoothers integrated in a complete 3D solver present a significant engineering challenge, a novel approach is proposed that addresses these challenges systematically through a change to the solver’s execution model. Enabled by user-level threading paired with a set of data and communication abstractions, this approach permits seamless aggregation of communication in plane smoothers — directly reusing code for a 2D distributed multilevel cycle. Results show an effective reduction in communication costs for coarse-grid problems, and result in a speedup of 8.7x in smoothing routines shown in Fig. 12 using this approach. This produces a significant improvement to strong scalability while maintaining favorable weak scaling behavior. Finally, a parallel scaling study using a series of refined meshes is included that demonstrates the effectiveness of this approach in an application of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Sub-melt nanosecond pulsed-laser induced densification and strain-field relaxation in single-crystal diamond

Dislocations and polishing-induced defect networks in synthetic diamond introduce local strain fields and broaden Raman features, limiting performance in optical, thermal, and electronic applications. Laser annealing is emerging as a promising approach to repair surface and near-surface defects in diamond without entering the melt regime, yet surface densification, defect-state modification, and associated structural changes have not been well quantified. In this work, we show that sub-melt nanosecond pulsed-laser annealing (PLA) induces near-surface densification and defect-mediated strain relaxation in single-crystal Chemical Vapor Deposition (CVD) diamond. Single- and two-pulse PLA were applied, and structural evolution was quantified using co-registered ISO 25,178 white-light interferometry, depth-resolved Raman spectroscopy, and cross-sectional STEM with geometric phase analysis (GPA). Across a 5 × 6 grid (n = 30), responsive regions exhibit large reductions in local slope (Sdq 45–65%), developed area (Sdr 60–90%), height spread (Sp, Sz 30–65%), void volume (Vv 57–60%), and roughness amplitude (Sa, Sq 48–57%), consistent with densification of ∼4–6.5 nm. Raman profiling shows narrowing of the diamond line and improved spectral uniformity to depths of ∼2–3 μm. Given that the Raman probing depth significantly exceeds the densified layer thickness, this response is interpreted as consistent with long-range strain-field redistribution originating from the near-surface region. STEM-GPA strain maps further support this interpretation, showing smoother strain fields, suppressed hotspots, and redistribution of localized strain concentrations following PLA. These results are consistent with defect-mediated strain relaxation and densification-driven modification of the near-surface energy state. The approach provides a scalable pathway for improving near-surface structural quality in diamond relevant to electronic, photonic, and quantum applications.

Areal surface metrology (ISO 25,178)↗

DOE OSTI2026

Propulsion System Design using a Dual 3-Phase PM Synchronous Reluctance Machine with X-Type Multi-Level GaN Inverter

— A propulsion system design is exhibited here that comprises of an X-type GaN power module based dual multi-level inverter and a PM Synchronous Reluctance motor. With the critical benefits of multi-level operation, namely low common mode EMI noise, low switching loss, low current Total Harmonic Distortion (THD), smoother torque and lower iron loss, this topology targets high system-level efficiency and high power density while using reduced rare earth (RE) elements in its motor. General Motors and Purdue University jointly designed and developed this 800V class, highly scalable traction drive that can deliver 200+ kW of power suitable for C-SUV to truck vehicle class. The 3-phase electric machine design utilizes dual winding with 6 terminals to work in line with the GaN X-type inverter, and results in a tractive solution that ensures higher machine efficiency while reducing cost and uncertainty related to use and availability of heavy rare earth/rare earth elements in its rotor.

MOMEN, FAIZUL [General Motors LLC, Detroit, MI (Un↗