Pub Date : 2019-09-01DOI: 10.1109/synasc49474.2019.00005
This volume contains papers selected from those presented at the 21th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) held in Timişoara, Romania from 4 to 7 September 2019. SYNASC is a series of annual events that aim to stimulate the interaction between the two scientific communities of symbolic and numeric computing and to present interesting applications of the algorithms developed in the areas both in theory and in practice. The choice of the symposium topic was motivated by the belief of the organizers that the dialogue between the two communities is very necessary for accelerating the progress in making the computer a truly intelligent aid for mathematicians and engineers.
{"title":"SYNASC 2019 Preface","authors":"","doi":"10.1109/synasc49474.2019.00005","DOIUrl":"https://doi.org/10.1109/synasc49474.2019.00005","url":null,"abstract":"This volume contains papers selected from those presented at the 21th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) held in Timişoara, Romania from 4 to 7 September 2019. SYNASC is a series of annual events that aim to stimulate the interaction between the two scientific communities of symbolic and numeric computing and to present interesting applications of the algorithms developed in the areas both in theory and in practice. The choice of the symposium topic was motivated by the belief of the organizers that the dialogue between the two communities is very necessary for accelerating the progress in making the computer a truly intelligent aid for mathematicians and engineers.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121869642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00022
David Damestani, L. Kovács, M. Suda
We describe recent extensions to the first-order theorem prover Vampire for proving theorems in the theory of fixed-sized bitvectors, possibly with quantifiers. Details are given on extending both the parser of Vampire as well as the theory reasoning framework of Vampire. We present our experimental results by evaluating and comparing our approach to SMT solvers. Our experiments report also on a few examples that can be solved only by our work.
{"title":"Superposition Reasoning about Quantified Bitvector Formulas","authors":"David Damestani, L. Kovács, M. Suda","doi":"10.1109/SYNASC49474.2019.00022","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00022","url":null,"abstract":"We describe recent extensions to the first-order theorem prover Vampire for proving theorems in the theory of fixed-sized bitvectors, possibly with quantifiers. Details are given on extending both the parser of Vampire as well as the theory reasoning framework of Vampire. We present our experimental results by evaluating and comparing our approach to SMT solvers. Our experiments report also on a few examples that can be solved only by our work.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114267416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00051
R. Marginean, A. Andreica, L. Dioşan, Z. Bálint
In this paper, we introduce Competitive Unsupervised GrowCut, a cellular automata-based, unsupervised and autonomous algorithm that combines the label merging component of Unsupervised GrowCut with the soft label propagation mechanism of GrowCut. We evaluated our algorithm on two benchmark image segmentation datasets, along with two related methods proposed in the literature. We also provide a detailed comparative analysis of the three algorithms' segmentation performance and properties. Our analysis identified application-specific regimes that govern the relative performance of the analyzed algorithms.
{"title":"Autonomous Image Segmentation by Competitive Unsupervised GrowCut","authors":"R. Marginean, A. Andreica, L. Dioşan, Z. Bálint","doi":"10.1109/SYNASC49474.2019.00051","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00051","url":null,"abstract":"In this paper, we introduce Competitive Unsupervised GrowCut, a cellular automata-based, unsupervised and autonomous algorithm that combines the label merging component of Unsupervised GrowCut with the soft label propagation mechanism of GrowCut. We evaluated our algorithm on two benchmark image segmentation datasets, along with two related methods proposed in the literature. We also provide a detailed comparative analysis of the three algorithms' segmentation performance and properties. Our analysis identified application-specific regimes that govern the relative performance of the analyzed algorithms.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123675271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00017
Daniel A. Brake, Noah S. Daleo, J. Hauenstein, Samantha N. Sherman
Minimizing the Euclidean distance (ℓ2 -norm) from a given point to the solution set of a given system of polynomial equations can be accomplished via critical point techniques. This article extends critical point techniques to minimization with respect to Hamming distance (ℓ0-"norm") and taxicab distance (ℓ1 -norm). Numerical algebraic geometric techniques are derived for computing a finite set of real points satisfying the polynomial equations which contains a global minimizer. Several examples are used to demonstrate the new techniques.
{"title":"Solving Critical Point Conditions for the Hamming and Taxicab Distances to Solution Sets of Polynomial Equations","authors":"Daniel A. Brake, Noah S. Daleo, J. Hauenstein, Samantha N. Sherman","doi":"10.1109/SYNASC49474.2019.00017","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00017","url":null,"abstract":"Minimizing the Euclidean distance (ℓ2 -norm) from a given point to the solution set of a given system of polynomial equations can be accomplished via critical point techniques. This article extends critical point techniques to minimization with respect to Hamming distance (ℓ0-\"norm\") and taxicab distance (ℓ1 -norm). Numerical algebraic geometric techniques are derived for computing a finite set of real points satisfying the polynomial equations which contains a global minimizer. Several examples are used to demonstrate the new techniques.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121075875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00034
Mara-Renata Petrusel, Sergiu Limboi
Most users often find themselves in a situation when they need to answer the same question: which product, movie, vacation offer, restaurant or book is the best to choose? In order to answer this question, Recommendation Systems have been developed to generate the best suggestions according to the user's interest. Recommendation Systems play an important role in the user's decision-making process by enriching its experience and satisfaction, considering his peers' actions and preferences. The goal of this paper is to enhance the recommendation process by applying Sentiment Analysis techniques on the input data. Sentiment Analysis is a domain that focuses on classifying information into positive, negative and neutral opinions. The results of a Sentiment Analysis task can be used to define social tendencies, items' popularity and adapting the services for users' needs. The proposed approach combines Sentiment Analysis and Recommendation Systems for defining the best suggestions for a user. Sentiment Analysis is applied for classifying restaurants' text-based reviews into positive and negative. The output of the Sentiment Analysis task is passed to a recommendation system that, using the collaborative filtering algorithm, will predict the rating for a not-visited restaurant and generate a list of top-n restaurants for the user. This approach outperformed the results obtained when the Sentiment Analysis step was not considered in the recommendation process. Therefore, the proposed system increases the accuracy of the recommended items by analyzing, from a sentiment point of view, the text-based reviews offered by users.
{"title":"A Restaurants Recommendation System: Improving Rating Predictions Using Sentiment Analysis","authors":"Mara-Renata Petrusel, Sergiu Limboi","doi":"10.1109/SYNASC49474.2019.00034","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00034","url":null,"abstract":"Most users often find themselves in a situation when they need to answer the same question: which product, movie, vacation offer, restaurant or book is the best to choose? In order to answer this question, Recommendation Systems have been developed to generate the best suggestions according to the user's interest. Recommendation Systems play an important role in the user's decision-making process by enriching its experience and satisfaction, considering his peers' actions and preferences. The goal of this paper is to enhance the recommendation process by applying Sentiment Analysis techniques on the input data. Sentiment Analysis is a domain that focuses on classifying information into positive, negative and neutral opinions. The results of a Sentiment Analysis task can be used to define social tendencies, items' popularity and adapting the services for users' needs. The proposed approach combines Sentiment Analysis and Recommendation Systems for defining the best suggestions for a user. Sentiment Analysis is applied for classifying restaurants' text-based reviews into positive and negative. The output of the Sentiment Analysis task is passed to a recommendation system that, using the collaborative filtering algorithm, will predict the rating for a not-visited restaurant and generate a list of top-n restaurants for the user. This approach outperformed the results obtained when the Sentiment Analysis step was not considered in the recommendation process. Therefore, the proposed system increases the accuracy of the recommended items by analyzing, from a sentiment point of view, the text-based reviews offered by users.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122732666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00028
Ciprian-Alin Simion, Dragos Gavrilut, H. Luchian
Cyber-Security industry has always been a "cat and a mouse" game - whenever a new technology was developed it was shortly followed by the appearance of several techniques used by malware creators to avoid detection. It is no surprise that the developing of adversarial machine learning algorithms has provided a tool that can be used to avoid machine learning based detection mechanisms available in security products. This paper presents how the same algorithms can also be used to strengthen a security solution by identifying its weak points / features. We will also provide a method that can be used to fight Generative Adversarial Networks (GANs) with GANs, that is effective when a malware writer is using these methods to avoid detection.
{"title":"An Adversarial Machine Learning Approach to Evaluate the Robustness of a Security Solution","authors":"Ciprian-Alin Simion, Dragos Gavrilut, H. Luchian","doi":"10.1109/SYNASC49474.2019.00028","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00028","url":null,"abstract":"Cyber-Security industry has always been a \"cat and a mouse\" game - whenever a new technology was developed it was shortly followed by the appearance of several techniques used by malware creators to avoid detection. It is no surprise that the developing of adversarial machine learning algorithms has provided a tool that can be used to avoid machine learning based detection mechanisms available in security products. This paper presents how the same algorithms can also be used to strengthen a security solution by identifying its weak points / features. We will also provide a method that can be used to fight Generative Adversarial Networks (GANs) with GANs, that is effective when a malware writer is using these methods to avoid detection.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130520081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00010
A. Gurfinkel, N. Bjørner
Constrained Horn Clauses (CHC) is a fragment of First Order Logic modulo constraints that captures many program verification problems as constraint solving. Safety verification of sequential programs, modular verification of concurrent programs, parametric verification, and modular verification of synchronous transition systems are all naturally captured as a satisfiability problem for CHC modulo theories of arithmetic and arrays. In general, the satisfiability of CHC modulo theory of arithmetic is undecidable. Thus, solving them is a mix of science, art, and a dash of magic. In this tutorial, we explore several aspects of this problem. First, we illustrate how different problems are translated to CHC. Second, we present a framework, called Spacer, that reduces symbolically solving Horn clauses to multiple simpler Satisfiability Modulo Theories, SMT, queries. Third, we describe advances in SMT that are necessary to make the framework a reality.
{"title":"The Science, Art, and Magic of Constrained Horn Clauses","authors":"A. Gurfinkel, N. Bjørner","doi":"10.1109/SYNASC49474.2019.00010","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00010","url":null,"abstract":"Constrained Horn Clauses (CHC) is a fragment of First Order Logic modulo constraints that captures many program verification problems as constraint solving. Safety verification of sequential programs, modular verification of concurrent programs, parametric verification, and modular verification of synchronous transition systems are all naturally captured as a satisfiability problem for CHC modulo theories of arithmetic and arrays. In general, the satisfiability of CHC modulo theory of arithmetic is undecidable. Thus, solving them is a mix of science, art, and a dash of magic. In this tutorial, we explore several aspects of this problem. First, we illustrate how different problems are translated to CHC. Second, we present a framework, called Spacer, that reduces symbolically solving Horn clauses to multiple simpler Satisfiability Modulo Theories, SMT, queries. Third, we describe advances in SMT that are necessary to make the framework a reality.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131633511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00021
Gergely Kovásznai, Krisztián Gajdár, L. Kovács
Wireless Sensor Networks (WSNs) serve as the basis for Internet of Things applications. A WSN consists of a number of spatially distributed sensor nodes, which cooperatively monitor physical or environmental conditions. In order to ensure the dependability of WSN functionalities, several reliability and security requirements have to be fulfilled. In previous work, we applied OMT (Optimization Modulo Theories) solvers to maximize a WSN's lifetime, i.e., to generate an optimal sleep/wake-up scheduling for the sensor nodes. We discovered that the bottleneck for the underlying SMT (Satisfiability Modulo Theories) solvers was typically to solve satisfiable instances. In this paper, we encode the WSN verification problem as a set of Boolean cardinality constraints, therefore SAT solvers can also be applied as underlying solvers. We have experimented with different SAT solvers and also with different SAT encodings of Boolean cardinality constraints. Based on our experiments, the SAT-based approach is very powerful on satisfiable instances, but quite poor on unsatisfiable ones. In this paper, we apply both SAT and SMT solvers in a portfolio setting. Based on our experiments, the MiniCARD+Z3 setting can be considered to be the most powerful one, which outperforms OMT solvers by 1-2 orders of magnitude.
{"title":"Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization","authors":"Gergely Kovásznai, Krisztián Gajdár, L. Kovács","doi":"10.1109/SYNASC49474.2019.00021","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00021","url":null,"abstract":"Wireless Sensor Networks (WSNs) serve as the basis for Internet of Things applications. A WSN consists of a number of spatially distributed sensor nodes, which cooperatively monitor physical or environmental conditions. In order to ensure the dependability of WSN functionalities, several reliability and security requirements have to be fulfilled. In previous work, we applied OMT (Optimization Modulo Theories) solvers to maximize a WSN's lifetime, i.e., to generate an optimal sleep/wake-up scheduling for the sensor nodes. We discovered that the bottleneck for the underlying SMT (Satisfiability Modulo Theories) solvers was typically to solve satisfiable instances. In this paper, we encode the WSN verification problem as a set of Boolean cardinality constraints, therefore SAT solvers can also be applied as underlying solvers. We have experimented with different SAT solvers and also with different SAT encodings of Boolean cardinality constraints. Based on our experiments, the SAT-based approach is very powerful on satisfiable instances, but quite poor on unsatisfiable ones. In this paper, we apply both SAT and SMT solvers in a portfolio setting. Based on our experiments, the MiniCARD+Z3 setting can be considered to be the most powerful one, which outperforms OMT solvers by 1-2 orders of magnitude.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126238770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00035
Maria Nutu, Horia F. Pop, C. Martis, S. Cosman, Andreea-Mǎdǎlina Nicorici
This paper presents two approaches of model order reduction applied to two different type of electrical motors, the Permanent Magnet Synchronous Reluctance Machine (PMASynRM) and the Switched Reluctance Motor(SRM). In the field of Electrical Machines, a motor can be described using a mathematical model, with complex non-linear differential equations, based on equivalent electric circuit parameters (inductances and resistances). Different theoretical and experimental methods have been proposed for estimating the inductances, requiring time consuming tests or simulations. Finding methods to reduce the number of simulations/measurements necessary to compute the parameters of the motors represents a constant concern in the Industry research field. Less measurements/simulations means reducing the computation time, which is a priority in Industry, for a shorter time-to-market. In our experiments we have chosen to reduce the problem dimensions for the computation of the magnetization characteristic of the machines, using Machine Learning. We compared Principal Component Analysis with Polynomial Interpolation and we have reduced the problem space with 50% up to 80%, depending on the motor type and context.
{"title":"A Machine Learning Perspective for Order Reduction in Electrical Motors Modeling","authors":"Maria Nutu, Horia F. Pop, C. Martis, S. Cosman, Andreea-Mǎdǎlina Nicorici","doi":"10.1109/SYNASC49474.2019.00035","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00035","url":null,"abstract":"This paper presents two approaches of model order reduction applied to two different type of electrical motors, the Permanent Magnet Synchronous Reluctance Machine (PMASynRM) and the Switched Reluctance Motor(SRM). In the field of Electrical Machines, a motor can be described using a mathematical model, with complex non-linear differential equations, based on equivalent electric circuit parameters (inductances and resistances). Different theoretical and experimental methods have been proposed for estimating the inductances, requiring time consuming tests or simulations. Finding methods to reduce the number of simulations/measurements necessary to compute the parameters of the motors represents a constant concern in the Industry research field. Less measurements/simulations means reducing the computation time, which is a priority in Industry, for a shorter time-to-market. In our experiments we have chosen to reduce the problem dimensions for the computation of the magnetization characteristic of the machines, using Machine Learning. We compared Principal Component Analysis with Polynomial Interpolation and we have reduced the problem space with 50% up to 80%, depending on the motor type and context.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122002438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-01DOI: 10.1109/SYNASC49474.2019.00019
K. Szerszeń, E. Zieniuk
The paper presents the integration of CAD models based on T-splines with the Parametric Integral Equation System (PIES) for solving 3D boundary value problems (BVP). T-splines will be used to generate the boundary of the BVP domain and their shape is modeled in the CAD system Rhino. In order to apply PIES, T-spline surfaces are converted into Bézier patches. The proposed strategy has been tested for problems modeled by Laplace's equation.
{"title":"Application of T-Splines and Bézier Extraction for Boundary Description in Parametric Integral Equation System for 3D Laplace's Equation","authors":"K. Szerszeń, E. Zieniuk","doi":"10.1109/SYNASC49474.2019.00019","DOIUrl":"https://doi.org/10.1109/SYNASC49474.2019.00019","url":null,"abstract":"The paper presents the integration of CAD models based on T-splines with the Parametric Integral Equation System (PIES) for solving 3D boundary value problems (BVP). T-splines will be used to generate the boundary of the BVP domain and their shape is modeled in the CAD system Rhino. In order to apply PIES, T-spline surfaces are converted into Bézier patches. The proposed strategy has been tested for problems modeled by Laplace's equation.","PeriodicalId":102054,"journal":{"name":"2019 21st International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129496352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：