In this paper, we present a serverless workflow execution system (DEWE v31) with Function-as-a-Service (FaaS aka serverless computing) as the target execution environment. DEWE v3 is designed to address problems of (1) execution of large-scale scientific workflows and (2) resource underutilization. At its core is our novel hybrid (FaaS and dedicated/local clusters) job dispatching approach taking into account resource consumption patterns of different phases of workflow execution. In particular, the hybrid approach deals with the maximum execution duration limit, memory limit, and storage space limit. DEWE v3 significantly reduces the efforts needed to execute large-scale scientific workflow applications on public clouds. We have evaluated DEWE v3 on both AWS Lambda and Google Cloud Functions and demonstrate that FaaS offers an ideal solution for scientific workflows with complex precedence constraints. In our large-scale evaluations, the hybrid execution model surpasses the performance of the traditional cluster execution model with significantly less execution cost.