Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations

Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used

Simulating earthquake scenarios in the European Project LESSLOSS: the case of the metropolitan area of Lisbon (MAL)

In the framework of the ongoing European project “LESSLOSS – Risk Mitigation for Earthquakes and Landslides” two sub-projects are devoted to earthquake disaster scenario predictions and loss modeling for urban areas and infrastructures. This paper is dealing with the sub-project 10, SP10, Task Programme “Scenario earthquake definitions for three cities”. Finite-fault seismological models are proposed to compute the earthquake scenarios for three urban areas – Istanbul (Turkey), Lisbon (Portugal) and Thessaloniki (Greece). For each case study, ground motion scenarios are developed for the most probable two events with different return periods, locations and magnitudes derived from historical and geological data. In this study, we simulate the accelerometric time series and response spectra for high frequency ground motion in the city of Lisbon and surrounding counties (Metropolitan Area of Lisbon), using two possible earthquake models: the inland source area of Lower Tagus Valley, M 5.7 (4.7) and a hypothesis of the offshore source area of the 1755 Lisbon, M 7.6. The non-stationary stochastic method RSSIM (Carvalho et al. 2004) and a new hybrid stochastic-deterministic approach, DSM (Pacor et al., 2005) are used in order to evaluate the ground shaking and to characterize its spatial variability. Then the site effects are evaluated by means of an equivalent stochastic non-linear one-dimensional ground response analysis of stratified soil profile units properly designed. Results are here presented in terms of PGA maps, for offshore and inland scenarios. The mean and worst shaking scenarios for the Metropolitan Area of Lisbon have been delineated at the bedrock. Local effects amplify the synthetic PGA values by approximately a factor of 2. This means that PGA values computed for bedrock in Lisbon city can increase from 0.12g up to 0.25g and up to 0.5g in surroundings, for the inland scenario, and from 0.045g up to 0.090g for a M7.6 offshore scenario