## 1 Introduction  
Since large interaction effects between structures and soil appear in heavy structures such as nuclear power plants and LNG storage tanks, the dynamic soil-structure interaction (SSI) is considered without fail in seismic design [1]. According to the ASCE 4, SSI effects can be neglected for a hard rock condition with shear wave velocity is greater than or equal to 2550 m/s (=8500 ft/s) (a rare case in practice). Therefore, the continuously increasing need for seismic designs that consider SSI can be accomplished using the frequency and time domain analysis methods. The frequency domain analysis approach approximates both structure and soil as linear viscoelastic bodies, performs independent analyses for discrete frequencies, and then converts the frequency response into the time domain to calculate the structure and soil responses [2]. This method has been combined with various other approaches, including the finite element, boundary element, boundary integral [3], and flexible volume methods [4], and has been used effectively in practice since the 1970s. SASSI (System for Analysis of Soil-Structure Interaction) is used worldwide as representative commercial software for the frequency domain analysis [4; 5; 6; 7]. Although analyzing the SSI time domain is generally more expensive than frequency domain analysis, it can be effective for analyzing the nonlinear response history, which cannot be handled accurately using frequency domain analysis. Currently, time domain analysis is generally carried out using finite elements for the nonlinear structures as well as near-field and far-field soil models in which boundary condition elements such as viscous boundaries, perfectly matched discrete layers, and perfectly matched layers are used to simulate the effects of infinite soil domain [8; 9; 10]. General-purpose finite element analysis software is effective at describing the nonlinear behavior of structures and soil. However, a numerical model for the time domain SSI analysis was verified by comparing time-domain solutions for a small seismic input with those obtained using the corresponding frequency domain technique [1; 11]. This is one of the reasons why more efficient frequency domain technologies are being developed. Moreover, the development of multi-core CPUs and parallel computational programming technologies, such as open multi-processing (OpenMP), message passing interface (MPI), coarray, and the Fortran compiler's DO CONCURRENT construct, has enabled cost-effective analyses of more complex models with shorter computation times [12; 13; 14]. Table 1 shows a comparison of the advantages and disadvantages of these methods [15]. In OpenMP, parallelization is performed using a shared memory method that uses computer resources (core and internal memory) to perform operations simultaneously. MPI is considered as the best parallelization technique in terms of analysis rate improvement and memory management because it has been continuously upgraded since its inception to configure multiple computers simultaneously as a single computer; the computers perform tasks independently of each other and share data through internal communication [13]. However, the method is rather inefficient because a construct different from the standard Fortran is required for communication between the computers, so that the entire source code needs to be modified to enable parallelization. The DO CONCURRENT construct has been used since Fortran 2008 as a simple replacement for the DO loop construct to express loop-level parallelism [16; 17], with the intent of enabling more effective automatic parallel execution. However, it was found that the performance is poor [15; 18]. The coarray method avoids the complexity of MPI and enables gradual parallelization of the existing source codes. This method has been adopted as a standard for Fortran compilers since Fortran 2008 [16; 17]. Coarray Fortran (CAF) has been widely applied in recent years as it facilitates the parallelization of the existing source codes [19; 20].