<p>This thesis deals with the development of efficient and reliable algorithms and library software for factorizing matrices and solving matrix equations on high-performance computer systems. The architectures of today's computers consist of multiple processors, each with multiple functional units. The memory systems are hierarchical with several levels, each having different speed and size. The practical peak performance of a system is reached only by considering all of these characteristics. One portable method for achieving good system utilization is to express a linear algebra problem in terms of level 3 BLAS (Basic Linear Algebra Subprogram) transformations. The most important operation is GEMM (GEneral Matrix Multiply), which typically defines the practical peak performance of a computer system. There are efficient GEMM implementations available for almost any platform, thus an algorithm using this operation is highly portable.</p><p>The dissertation focuses on how recursion can be applied to solve linear algebra problems. Recursive linear algebra algorithms have the potential to automatically match the size of subproblems to the different memory hierarchies, leading to much better utilization of the memory system. Furthermore, recursive algorithms expose level 3 BLAS operations, and reveal task parallelism. The first paper handles the Cholesky factorization for matrices stored in packed format. Our algorithm uses a recursive packed matrix data layout that enables the use of high-performance matrix--matrix multiplication, in contrast to the standard packed format. The resulting library routine requires half the memory of full storage, yet the performance is better than for full storage routines.</p><p>Paper two and tree introduce recursive blocked algorithms for solving triangular Sylvester-type matrix equations. For these problems, recursion together with superscalar kernels produce new algorithms that give 10-fold speedups compared to existing routines in the SLICOT and LAPACK libraries. We show that our recursive algorithms also have a significant impact on the execution time of solving unreduced problems and when used in condition estimation. By recursively splitting several problem dimensions simultaneously, parallel algorithms for shared memory systems are obtained. The fourth paper introduces a library---RECSY---consisting of a set of routines implemented in Fortran 90 using the ideas presented in paper two and three. Using performance monitoring tools, the last paper evaluates the possible gain in using different matrix blocking layouts and the impact of superscalar kernels in the RECSY library. </p>

This thesis deals with the development of efficient and reliable algorithms and library software for factorizing matrices and solving matrix equations on high-performance computer systems. The architectures of today's computers consist of multiple processors, each with multiple functional units. The memory systems are hierarchical with several levels, each having different speed and size. The practical peak performance of a system is reached only by considering all of these characteristics. One portable method for achieving good system utilization is to express a linear algebra problem in terms of level 3 BLAS (Basic Linear Algebra Subprogram) transformations. The most important operation is GEMM (GEneral Matrix Multiply), which typically defines the practical peak performance of a computer system. There are efficient GEMM implementations available for almost any platform, thus an algorithm using this operation is highly portable. The dissertation focuses on how recursion can be applied to solve linear algebra problems. Recursive linear algebra algorithms have the potential to automatically match the size of subproblems to the different memory hierarchies, leading to much better utilization of the memory system. Furthermore, recursive algorithms expose level 3 BLAS operations, and reveal task parallelism. The first paper handles the Cholesky factorization for matrices stored in packed format. Our algorithm uses a recursive packed matrix data layout that enables the use of high-performance matrix--matrix multiplication, in contrast to the standard packed format. The resulting library routine requires half the memory of full storage, yet the performance is better than for full storage routines. Paper two and tree introduce recursive blocked algorithms for solving triangular Sylvester-type matrix equations. For these problems, recursion together with superscalar kernels produce new algorithms that give 10-fold speedups compared to existing routines in the SLICOT and LAPACK libraries. We show that our recursive algorithms also have a significant impact on the execution time of solving unreduced problems and when used in condition estimation. By recursively splitting several problem dimensions simultaneously, parallel algorithms for shared memory systems are obtained. The fourth paper introduces a library---RECSY---consisting of a set of routines implemented in Fortran 90 using the ideas presented in paper two and three. Using performance monitoring tools, the last paper evaluates the possible gain in using different matrix blocking layouts and the impact of superscalar kernels in the RECSY library.

Brandskyddet hos nya och gamla konstruktioner har blivit en väsentlig del av byggnadens säkerhet de senaste 70 åren. En av byggnadstyperna med högst skydd i form av brandskydd är sjukhus. I Sverige har sjukhus en generellt hög säkerhet, detta eftersom vissa personer har svårt att röra sig eller till och med är nedsövda. Även om dimensioneringen av dagens sjukhus utgår från ett högt brandskydd och säkerhetstänk, kan det finnas brister i det befintliga brandskyddet.   Examensarbetet syftar till att undersöka om luftslussens funktion avseende brandskydd mellan vårdavdelningar på sjukus och om de uppfyller den funktion som beskrivs i dagens regelverk. Detta kontrollerades genom att genomföra en litteraturstudie om varför och hur luftslussen har den funktion som den har idag. Det visar sig att under de senaste 25 åren har luftslussen i regelverken inte utvecklats. När bakgrundsinformationen var hämtad, genomfördes ett studiebesök på ett sjukhus där utrymningsövning med säng gjordes. Anledningen till detta var att beräkna medelhastighet för utrymning med säng och tid respektive dörr är öppen i luftslussen samt hur lång tid det tar att utrymma för att sedan återinträda till vårdnadssalen. Baserat på dessa tider gjordes sedan sex stycken databeräkningar med olika brandeffekter. Effekterna gjordes med och utan sprinkler samt med och utan luftsluss.   De sex CFD-beräkningarna delades in i tre fall. Det första fallet var en sängbrand med 800 kW som brandeffekt. Andra och tredje fallet illustrerade en 5 MW brand som effekt där ena fallet var med sprinkler och det andra utan. Varje fall bestod av två databeräkningar, ena beräkningen var med en luftsluss där dörrarna hade samma funktion som de hade på sjukhuset. Den andra var enbart med en dörr istället för luftsluss.   Utdatafilerna analyserades och jämfördes med varandra, först mot fallet med eller utan luftsluss och sedan mot de olika brandeffekterna. Detta gjordes för att se om någon brandgasspridning skedde beroende på om det var luftsluss eller ej och vid vilken brandeffekt samt tid brandgasspridning sker.   Resultaten visar att i alla databeräkningarna sker det brandgasspridning till intilliggande brandcell oavsett om det är luftsluss eller ej. Den enda modellen som luftslussen medför ett visst skydd mot brandgasspridning är vid sängbranden, men det är endast vid första passagen vilket ej kan anses uppfylla kravet.   Eftersom detta är en brist i de befintliga brandskyddsreglerna om hur ett sjukhus ska dimensioneras gällande luftslussarnas utformning, bör revideringar ske då brandgasspridning äger rum oavsett om det är luftsluss eller ej. För att personer ska känna sig säkra gällande skydd mot bränder bör ett bra brandskydd vara upprättat. Ett alternativ som används idag istället för luftsluss är att endast ha en brandklassad dörr, och sedan trycksätta intilliggande brandcell så ej brandgasen sprider sig. / For the past 70 years the safety protection of new and old construction has become very substantially, especially regarding fire protection. In form of fire protection, one of the most protective buildings is hospitals. In Sweden, hospitals has a generally high safe protection. People that are visiting the hospital could be visitors, victims or even anesthetized so the fire safety is important.   The purpose of this report is to investigate if the airlock functions at Swedish hospitals between different care sections fulfill the regulations. A literature study was made to understand why the regulations regarding airlocks at hospitals are formed the way they are. It resulted in that the regulations regarding airlocks haven’t been changed for the past 25 years. The report continued with a visit to a local hospital. An evacuation with hospital beds was made to gather information to the CFD calculations to know how the airlock doors was operating. The process was to start the evacuation based on a timer and stop the clock when the staff returned through the first door of the airlock and waited for the door to close.   A room was programmed in Pyrosim based on a real hospital section with an airlock that connected two rooms. The programming was based on the evacuation. Totally there were six CFD calculations with three different cases. Two different effects was used to illustrate the fire. A 800 kW hospital bed fire and two with the effect of 5 MW, one with sprinkler and the other without. The purpose of the data analysis was to investigate smoke movements and penetration within hospital facilities.   The data calculations showed that all 6 of the cases failed and smoke was penetrated through the airlock. Only one of the cases was able to withstand to 300 seconds and the other one failed at the first passage.   The results shows that there are a deficiency in the current regulation accordning the fire safety. An alternative that is used today when projecting a hospital, is to replace the airlock with a door and pressurize the room next door so that the smoke won’t spread as fast. Although pressurized rooms are used today, they need to be tested if they work. And if they do, be replacing the currently used airlocks.

I dagens läge har energifrågorna väckt ett stort intresse i samhället. Nu fokuseras det mer på att bygga energisnålare hus. En betydande faktor som påverkar energiförbrukningen i våra hus är köldbryggor. De uppstår då ett material med dålig värmeisolering bryter igenom ett material med bättre värmeisolering. Köldbryggor är nästan omöjligt att undvika, dock går alltid att reducera. I praktiken är det ofta inte möjligt att helt undvika köldbryggor, men det finns många olika möjligheter att minska köldbryggeffekten kraftigt. Detta eftersträvas för att uppnå lägre energikostnader eftersom köldbryggor kan medföra en betydande ökning av värmeförlusten. Avgränsningen för detta examensarbete framgår av titeln Köldbryggors inverkan på isoleringsegenskaper för sandwichelement, anslutning mellan fönster och yttervägg. Den främsta metoden som används för att åstadkomma resultatet är PC-programmet HEAT2, men litteraturstudier har också använts. HEAT2 är ett tvådimensionellt värmeflödesprogram, som beräknar den värmemängd som leds genom konstruktionsdelen. Den bygger på att dela in byggnadsdelen i ett rutnät (mesh). Ju fler rutor den blir uppdelad i, desto noggrannare resultat, men beräkningen blir samtidigt mer tidskrävande att utföra. En särskild analys gjordes med och utan den dränerande skyddsplasten i fönstrets överkant då materialet skär igenom värmeisoleringen vid betongklacken. Plasten har mångfaldigt högre värmekonduktivitet än värmeisoleringen, men den är bara 1 mm tjock. Beräkningsresultaten visar att skyddsplasten gav en betydande skillnad. / Currently, the energy issues brought a lot of interest in the community. Now is the focus more on building energy-efficient houses. A significant factor influencing energy consumption in our buildings is thermal bridges. They occur when a material with poor thermal insulation breaks through a material with better insulation. In practice it is often not possible to avoid thermal bridges completely, but there are many different options to reduce the thermal bridge effect significantly. This is desirable in order to achieve lower energy costs because thermal bridges can lead to a significant increase in the heat losses. The limitation of this degree project is evident from the title Thermal bridges impact on the insulation properties of sandwich panels, the connection between the windows and external walls The primary means used to achieve the results is the HEAT2 PC-program, but literature studies were also used. HEAT2 is a two-dimensional heat flow program that calculates the amount of energy passed through the part of the construction. It is based on the allocation of the construction into a mesh, i.e. a grid. The more the mesh is divided into the more accurate the results, but the calculations are at the same time more time consuming to perform. A separate analysis was done with and without the draining protective plastic in the window's top edge where the material is passing through the thermal insulation at the concrete heel. The plastic has many orders of magnitude higher thermal conductivity than the thermal insulation, but it is only 1 mm thick. The calculation results show that the plastic caused a significant difference.