3-D magnetotelluric (MT) forward modeling has always been faced with the problems of high memory requirements and long computing time. In this article, we design a scalable parallel algorithm for 3-D MT finite element modeling in anisotropic media. The parallel algorithm is based on the distributed mesh storage, including multiple parallel granularities, and is implemented through multiple tools. Message-passing interface (MPI) is used to exploit process parallelisms for subdomains, frequencies, and solving equations. Thread parallelisms for merge sorting, element analysis, matrix assembly, and imposing Dirichlet boundary conditions are developed by Open Multi-Processing (OpenMP). We validate the algorithm through several model simulations and study the effects of topography and conductivity anisotropy on apparent resistivities and phase responses. Scalability tests are performed on the Tianhe-2 supercomputer to analyze the parallel performance of different parallel granularities. Three parallel direct solvers Supernodal LU (SUPERLU), MUltifrontal Massively Parallel sparse direct Solver (MUMPS), and Parallel Sparse matriX package (PASTIX) are compared in solving sparse systems of equations. As a result, reasonable parallel parameters are suggested for practical applications. The developed parallel algorithm is proven to be efficient and scalable.

Sparse Matrix-Vector Multiplication (SpMV) plays a crucial role in scientific computing, but severe load imbalance among threads restricts its performance. Previous load-balancing methods have primarily ignored the CPU’s cache line-based memory access characteristics and the impact of data locality during workload evaluation and partitioning, leading to limited effect in load balancing. To address this issue, we propose a cache-aware memory load-balancing SpMV algorithm, CAMLB-SpMV, based on the Compressed Sparse Row (CSR) format. We evaluate all memory access loads of CSR-based SpMV at the cache line level and utilize a sliding window to record accesses to x, enabling the load evaluation to perceive data locality. Finally, the total workload is evenly distributed to threads to achieve load-balancing. Experimental results on 2661 sparse matrices from SuiteSparse sparse matrix dataset demonstrate that CAMLB-SpMV surpasses Intel MKL, Merge-Based, CSR5-AVX512, and CVR by an average factor of 1.16x, 1.19x, 2.16x, and 1.17x (up to 13.77x, 7.45x, 15.89x, and 8.63x), respectively, on Intel Xeon Platinum 9242. Moreover, it outperforms AMD AOCL, Merge-Based, and CSR5-AVX2 by an average factor of 2.70x, 1.62x, and 3.40x (up to 25.03x, 4.36x, and 13.7x) on AMD EPYC 7542.

Structured grid-based sparse matrix-vector multiplication and Gauss–Seidel iterations are very important kernel functions in scientific and engineering computations, both of which are memory intensive and bandwidth-limited. GPDSP is a general purpose digital signal processor, which is a very significant embedded processor that has been introduced into high-performance computing. In this paper, we designed various optimization methods, which included a blocking method to improve data locality and increase memory access efficiency, a multicolor reordering method to develop Gauss–Seidel fine-grained parallelism, a data partitioning method designed for GPDSP memory structures, and a double buffering method to overlap computation and access memory on structured grid-based SpMV and Gauss–Seidel iterations for GPDSP. At last, we combined the above optimization methods to design a multicore vectorization algorithm. We tested the matrices generated with structured grids of different sizes on the GPDSP platform and obtained speedups of up to 41× and 47× compared to the unoptimized SpMV and Gauss–Seidel iterations, with maximum bandwidth efficiencies of 72% and 81%, respectively. The experiment results show that our algorithms could fully utilize the external memory bandwidth. We also implemented the commonly used mixed precision algorithm on the GPDSP and obtained speedups of 1.60× and 1.45× for the SpMV and Gauss–Seidel iterations, respectively.

The marine magnetotelluric (MMT) method is a significant tool extensively utilized in offshore studies, including the understanding of the Earth’s tectonics and hydrocarbon exploration. Conductive anisotropy and non-zero magnetic susceptibility are common phenomena observed in the Earth’s subsurface, and MMT forward modeling is the basis of practical inversion. However, numerical modeling that incorporates both conductive anisotropy and magnetic susceptibility has received limited attention. Moreover, both accuracy and efficiency are crucial in developing a 3D MMT modeling algorithm. Therefore, we developed a multi-level parallel MMT forward modeling algorithm that is capable of simultaneously modeling conductive and magnetic arbitrary anisotropic models using the vector finite element method based on the secondary field formula. The algorithm’s accuracy was validated through comparisons with previously published results for an arbitrary anisotropic model. The results show that the maximum relative error is below 2%, and the speedup reaches an impressive value of 552.41 when running with 2048 cores. Furthermore, the MMT responses of conductive anisotropy and magnetic susceptibility were comprehensively analyzed by several typical models. Our findings highlight the importance of considering magnetic susceptibility in magnetite-rich regions, particularly as the MMT responses may exhibit opposite responses for anomalies with lower resistivity and higher magnetic susceptibility compared with the surrounding rocks.

Efficient obstacle avoidance in urban 3D environments is a key challenge for Unmanned Aerial Vehicles (UAVs) in urban security, logistics, and environmental monitoring. Traditional path planning algorithms, such as A*, struggle in dynamic environments due to static heuristics, while the Dynamic Window Approach (DWA) often falls into local optima, causing inefficiencies and instability. Herein, we introduce the Pheromone-Guided Dynamic Window Approach (PG-DWA), a hybrid method that integrates global path planning with local obstacle avoidance. It utilizes a time-varying 3D pheromone field as shared environmental memory, encoding high-quality paths and high-risk areas with positive and negative pheromones to guide global path planning. The pheromone concentration and gradient are integrated into the DWA trajectory function, along with geometric projection, to balance target approach and safety for local dynamic obstacle avoidance, while smoothing the path during stable flight. Simulation results confirm the efficiency in 3D obstacle avoidance, alleviating stagnation and angular velocity oscillations in concave obstacles and narrow passages, ensuring smooth flight paths, leading to a 34% reduction in average flight time and a 53% increase in flight speed (from 0.984 m/s to 1.51 m/s). This significant improvement demonstrates an efficient and stable solution for UAV navigation in complex urban environments.