This study introduces a method to build a multi-domain matrix (MDM), visualizing the intended architecture of a system within the component, function, and parameter domains. The MDM is generated from textual function specifications that are subject to a specific grammatical structure and vocabulary based upon the functional basis and interaction basis as presented in the literature. Two types of functions are distinguished: functions specifying what functionality a particular component provides to another component, and functions specifying the internal working (transformation of flow) of a particular component. The fixed grammar for the specification of the two types of functions allows for the automated derivation of dependencies between components, between functions of components, and between system parameters. A case study on a navigation lock demonstrates that the system architecture generated from function specifications matches the architecture of the real lock system fairly well. As such the method can be used in the early design phase to reveal the product architecture that is embodied in the function specifications of system components. The method may also support modeling of high-definition DSMs of existing engineering systems.