Hybrid CPU-GPU modal frequency response solver performance and scaling improvements

Frequency-domain simulations of practical engineering systems require solving systems of complex linear algebraic equations with millions of equations for thousands of excitation frequency values. Direct or iterative solution at each frequency is not usually feasible because of the computational cost. The modal superposition method is widely used for solving large-scale linear dynamics problems. It includes extraction of the natural modes of vibration of the undamped system and solving the reduced system of equations of motion in the frequency domain. However, in practical engineering simulations such reduced systems of equations can have tens of thousands of complex linear equations and hundreds of right-hand-side vectors associated with multiple load cases. Therefore, solving for thousands of excitation frequencies still can be costly.

The hybrid CPU-GPU high performance modal frequency response solver was first introduced in Abaqus 2017. It utilizes multiple CPU cores of symmetric multiprocessing systems, together with a single general-purpose graphics processing unit (GPGPU). The following enhancements have been made to the hybrid modal frequency response solver in this release:

• Improved CPU scaling and GPU performance of the solution algorithms

• The use of multiple GPGPU devices together with all available CPU cores

Consider the frequency response analysis of a full car finite element model with 17.5 million degrees of freedom including the air in the cabin. Diagonal viscous modal damping is applied in the structural and acoustic domains, and material structural damping is applied in the structural and acoustic domains. Therefore, the imaginary part of the modal operator is a full dense matrix. The modal frequency response is calculated at 1,000 frequency points for 114 load cases using 10,818 uncoupled eigenmodes (10,502 structural; 316 acoustic). Timing data were obtained using a 28-core (2 × 14) Intel^® Xeon^® E5-2697 V3 machine with RAM 768 GB and two NVIDIA^® Tesla^® K80 GPU (K80: 2 × K40).

Figure 1 shows improved CPU scaling of the modal frequency response solver over the last two Abaqus releases. Figure 2 demonstrates the hybrid CPU-GPU modal frequency response solver scaling in Abaqus 2018. It shows the total time of the modal frequency response calculation using a different number of CPU cores and GPGPU devices.