Gotowa bibliografia na temat „Kernel-independent fast solvers”

Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics,H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solveH-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure ofH-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solvingH-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

A space-domain integral equation method accelerated with adaptive cross approximation (ACA) is presented for the fast and accurate analysis of electromagnetic (EM) scattering from multilayered metallic photonic crystal (MPC). The method directly solves for the electric field in order to easily enable the periodic boundary condition (PBC) in the spatial domain. The ACA is a purely algebraic method allowing the compression of fully populated matrices; hence, its formulation and implementation are independent of integral equation kernel (Green’s function). Therefore, the ACA is very well suited for accelerating integral equation analysis of periodic structure with the integral kernel of the periodic Green’s function (PGF). The computation of the spatial-domain periodic Green’s function (PGF) is accelerated by the modified Ewald transformation, such that the multilayered periodic structure can be analyzed efficiently and accurately. An effective interpolation method is also proposed to fast compute the periodic Green’s function, which can greatly reduce the time of matrix filling. Numerical examples show that the proposed method can greatly save the frequency sweep time for multilayered periodic structure.

AbstractThis paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New York, 2006) and Zeng et al. (Constr. Approx. 30: 529–555, 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver. The main contribution of the paper is the application to the approximation problem for uncertainty quantification of elliptic partial differential equations, with the diffusion coefficient given by a random field that is periodic in the stochastic variables, in the model proposed recently by Kaarnioja et al. (SIAM J Numer Anal 58(2): 1068–1091, 2020). The paper gives a full error analysis, and full details of the construction of lattices needed to ensure a good (but inevitably not optimal) rate of convergence and an error bound independent of dimension. Numerical experiments support the theory.

Coordination is essential in the design of dynamic control strategies for multi-arm robotic systems. Given the complexity of the task and dexterity of the system, coordination constraints can emerge from different levels of planning and control. Primarily, one must consider task-space coordination, where the robots must coordinate with each other, with an object or with a target of interest. Coordination is also necessary in joint space, as the robots should avoid self-collisions at any time. We provide such joint-space coordination by introducing a centralized inverse kinematics (IK) solver under self-collision avoidance constraints, formulated as a quadratic program and solved in real-time. The space of free motion is modeled through a sparse non-linear kernel classification method in a data-driven learning approach. Moreover, we provide multi-arm task-space coordination for both synchronous or asynchronous behaviors. We define a synchronous behavior as that in which the robot arms must coordinate with each other and with a moving object such that they reach for it in synchrony. In contrast, an asynchronous behavior allows for each robot to perform independent point-to-point reaching motions. To transition smoothly from asynchronous to synchronous behaviors and vice versa, we introduce the notion of synchronization allocation. We show how this allocation can be controlled through an external variable, such as the location of the object to be manipulated. Both behaviors and their synchronization allocation are encoded in a single dynamical system. We validate our framework on a dual-arm robotic system and demonstrate that the robots can re-synchronize and adapt the motion of each arm while avoiding self-collision within milliseconds. The speed of control is exploited to intercept fast moving objects whose motion cannot be predicted accurately.

Euler deconvolution of magnetic fields, induced by sheets with nonnegligible widths, provides source-location estimates that are biased away from the true locations. I have derived formulas for these biases and used the equations to model diffuse solution patterns that are owing to the interplay between integer structural indices and finite sources. These patterns closely match solutions deconvolved from aeromagnetic data over northern Canada. Motivated out of the necessity that complete harmonics be integral degreed, I have investigated and discovered the ineffectiveness of noninteger structural indices in remediating the aforementioned biases. In fact, real numbers impart similar errors to multiple Euler solutions, causing ensembles of estimated origin loci to reside below the middle of the tops of wide sheets. I have devised an approach requiring the inclusion of a term in the Euler deconvolution kernel whose independent variable is the second horizontal derivative of the total field, and whose partial slope (to be solved) is the sheet width. This approach is appropriate only if the thickness does not exceed the depth. However, precision could be sacrificed in favor of accuracy because of the presence of the second derivative. The application to aeromagnetic data over a diabase dike in northern Canada yields a depth effectively coincident with a drilling depth.

Driven by the abundant data generated from computational fluid dynamics (CFD) simulations, machine learning (ML) methods surpass the deterministic criteria on flow phenomena identification in the way that they are independent of a case-by-case threshold by combining the flow field properties and the topological distribution of the phenomena. The current most popular and successful ML models based on convolutional neural networks are limited to structured meshes and unable to directly digest the data generated from unstructured meshes, which are more widely used in real industrial CFD simulations. We proposed a framework based on graph neural networks with the proposed fast Gaussian mixture model as the convolution kernel and U-Net architecture to detect flow phenomena based on a graph hierarchy generated by the algebraic multigrid method embedded in the open-source CFD solver, code_saturne. We demonstrate the superiority of the proposed kernel and U-Net architecture, along with the generality of the framework to unstructured mesh and unseen case, on detecting the vortices once trained on a single backward-facing step case. Our proposed framework can be trivially extended to detect more flow phenomena in three dimensional cases, which is ongoing work.

In one of the earliest films about a whistleblower, On the Waterfront (1954), the dock worker Terry Malloy (Marlon Brando), who also works for the union boss and mobster Johnny Friendly (Lee J. Cobb), decides to testify in court against him and uncover corruption and murder. By doing so he will not only suffer retribution from Friendly but also be seen as a “stool pigeon” by his co-workers, friends, and neighbours who will shun him, and he will be “marked” forever by his deed. Nonetheless, he decides to do the right thing. Already it is clear that in most cases the whistleblowers are not simply the ones who reveal things, but they themselves are also revealed.My aim in this article is to explore the depiction of Edward Snowden and Julian Assange in fiction film and its connection to what I would like to call, with Slavoj Žižek, “Hollywood ideology”; the heroisation of the “ordinary guy” against a big institution or a corrupt individual, as it is the case in Snowden (2016) on the one hand, and at the same time the impossibility of true systemic critique when the one who is criticising is “outside of the system”, as Assange in The Fifth Estate (2013). Both films also rely on the notion of individualism and convey conflicting messages in regard to understanding the perception of whistleblowers today. Snowden and AssangeAlthough there are many so called “whistleblower films” since On the Waterfront, like Serpico (1973), All the President’s Men (1976), or Silkwood (1983), to name but a few (for a comprehensive list see https://ew.com/movies/20-whistleblower-movies-to-watch/?), in this article I will focus on the most recent films that deal with Edward Snowden and Julian Assange. These are the most prominent cases of whistleblowing in the last decade put to film. They are relevant today also regarding their subject matter—privacy. Revealing secrets that concern privacy in this day and age is of importance and is pertinent even to the current Coronavirus crisis, where the question of privacy again arises in form of possible tracking apps, in the age of ever expanding “surveillance capitalism” (Zuboff).Even if Assange is not strictly speaking a whistleblower, an engagement with his work in this context is indispensable since his outsider status, up to a point, resembles those of Snowden or Manning. They are not only important because they can be considered as “authentic heroe[s] of our time” (Žižek, Pandemic, 7), but also because of their depiction which differs in a very crucial way: while Snowden is depicted as a “classic” whistleblower (an American patriot who did his duty, someone from the “inside”), Assange’s action are coming from the outside of the established system and are interpreted as a selfish act, as it is stated in the film: “It was always about him.”Whistleblowers In his Whistleblower’s Handbook, Kohn writes: “who are these whistleblowers? Sometimes they are people you read about with admiration in the newspaper. Other times they are your co-workers or neighbours. However, most whistleblowers are regular workers performing their jobs” (Kohn, xi). A whistleblower, as the employee or a “regular worker”, can be regarded as someone who is a “nobody” at first, an invisible “cog in the wheel” of a certain institution, a supposedly devoted and loyal worker, who, through an act of “betrayal”, becomes a “somebody”. They do something truly significant, and by doing so becomes a hero to some and a traitor to others. Their persona suddenly becomes important.The wrongdoings that are uncovered by the whistleblower are for the most part not simply isolated missteps, but of a systemic nature, like the mass surveillance by the National Security Agency (NSA) uncovered by Snowden. The problem with narratives that deal with whistleblowing is that the focus inevitably shifts from the systemic problem (surveillance, war crimes, etc.) to the whistleblower as an individual. Moretti states that the interest of the media regarding whistleblowing, if one compares the reactions to the leaking of the “Pentagon Papers” regarding the Vietnam War in the 1970s by Daniel Ellsberg and to Snowden’s discoveries, shifted from the deed itself to the individual. In the case of Ellsberg, Moretti writes:the legitimate questions were not about him and what motivated him, but rather inquiry on (among other items) the relationship between government and media; whether the U.S. would be damaged militarily or diplomatically because of the release of the papers; the extent to which the media were acting as watchdogs; and why Americans needed to know about these items. (8)This shift of public interest goes along, according to Moretti, with the corporate ownership of media (7), where profit is the primary goal and therefore sensationalism is the order of the day, which is inextricably linked to the focus on the “scandalous” individual. The selfless and almost self-effacing act of whistleblowing becomes a narrative that constructs the opposite: yet another determined individual that through their sheer willpower achieves their goal, a notion that conforms to neoliberal ideology.Hollywood IdeologyThe endings of All the President’s Men and The Harder They Fall (1956), another early whistleblower film, twenty years apart, are very similar: they show the journalist eagerly typing away on his typewriter a story that will, in the case of the former, bring down the president of the United States and in the latter, bring an end to arranged fights in the boxing sport. This depiction of the free press vanquishing the evil doers, as Žižek states it, is exactly the point where “Hollywood ideology” becomes visible, which is:the ideology of such Hollywood blockbusters as All the President’s Men and The Pelican Brief, in which a couple of ordinary guys discover a scandal which reaches up to the president, forcing him to step down. Corruption is shown to reach the very top, yet the ideology of such works resides in their upbeat final message: what a great country ours must be, when a couple of ordinary guys like you and me can bring down the president, the mightiest man on Earth! (“Good Manners”)This message is of course part of Hollywood’s happy-ending convention that can be found even in films that deal with “serious” subject matters. The point of the happy end in this case is that before it is finally reached, the film can show corruption (Serpico), wrongdoings of big companies (The Insider, 1999), or sexual harassment (North Country, 2005). It is important that in the end all is—more or less—good. The happy ending need not necessarily be even truly “happy”—this depends on the general notion the film wants to convey (see for instance the ending of Silkwood, where the whistleblower is presumed to have been killed in the end). What is important in the whistleblower film is that the truth is out, justice has been served in one way or the other, the status quo has been re-established, and most importantly, there is someone out there who cares.These films, even when they appear to be critical of “the system”, are there to actually reassure their audiences in the workings of said system, which is (liberal) democracy supported by neoliberal capitalism (Frazer). Capitalism, on the other hand, is supported by the ideology of individualism which functions as a connecting tissue between the notions of democracy, capitalism, and film industry, since we are admiring exceptional individuals in performing acts of great importance. This, in turn, is encapsulated by the neoliberal mantra—“anyone can make it, only if they try heard enough”. As Bauman puts it more concretely, the risks and contradictions in a society are produced socially but are supposed to be solved individually (46).Individualism, as a part of the neoliberal capitalist ideology, is described already by Milton Friedman, who sees the individual as the “ultimate entity in the society” and the freedom of the individual as the “ultimate goal” within this society (12). What makes this an ideology is the fact that, in reality, the individual, or in the context of the market, the entrepreneur, is always-already tethered to and supported by the state, as Varoufakis has successfully proven (“Varoufakis/Chomsky discussion”). Therefore individualism is touted as an ideal to strive for, while for neoliberalism in order to function, the state is indispensable, which is often summed up in the formula “socialism for the rich, capitalism for the poor” (Polychroniou). The heroic Hollywood individual, as shown in the whistleblower film, regardless of real-life events, is the perfect embodiment of individualist ideology of neoliberal capitalism—we are not seeing a stylised version of it, a cowboy or a masked vigilante, but a “real” person. It is paradoxically precisely the realism that we see in such films that makes them ideological: the “based on a true story” preamble and all the historical details that are there in order to create a fulfilling cinematic experience. All of this supports its ideology because, as Žižek writes, “the function of ideology is not to offer us a point of escape from our reality but to offer us the social reality itself as an escape from some traumatic, real kernel” (Sublime Object 45). All the while Snowden mostly adheres to Hollywood ideology, The Fifth Estate also focuses on individualism, but goes in a different direction, and is more problematic – in the former we see the “ordinary guy” as the American hero, in the latter a disgruntled individual who reveals secrets of others for strictly personal reasons.SnowdenThere is an aspect of the whistleblower film that rings true and that is connected to Michel Foucault’s notion of power (“Truth and Power”). Snowden, through his employment at the NSA, is within a power relations network of an immensely powerful organisation. He uses “his” power, to expose the mass surveillance by the NSA. It is only through his involvement with this power network that he could get insight into and finally reveal what NSA is doing. Foucault writes that these resistances to power from the inside are “effective because they are formed right at the point where relations of power are exercised; resistance to power does not have to come from elsewhere to be real … It exists all the more by being in the same place as power” (Oushakine 206). In the case of whistleblowing, the resistance to power must come exactly from the inside in order to be effective since whistleblowers occupy the “same place as power” that they are up against and that is what in turn makes them “powerful”.Fig. 1: The Heroic Individual: Edward Snowden in SnowdenBut there is an underside to this. His “relationship” to the power structure he is confronting greatly affects his depiction as a whistleblower within the film—precisely because Snowden, unlike Assange, is someone from inside the system. He can still be seen as a patriot and a “disillusioned idealist” (Scott). In the film this is shown right at the beginning as Snowden, in his hotel room in Hong Kong, tells the documentary filmmaker Laura Poitras (Melissa Leo) and journalist Glenn Greenwald (Zachary Quinto) his name and who he is. The music swells and the film cuts to Snowden in uniform alongside other soldiers during a drill, when he was enlisted in the army before work for the NSA.Snowden resembles many of Stone’s typical characters, the all-American patriot being disillusioned by certain historical events, as in Born on the 4th of July (1989) and JFK (1991), which makes him question the government and its actions. It is generally of importance for a mainstream Hollywood film that the protagonist is relatable in order for the audiences to sympathise with them (Bordwell and Thompson 82). This is important not only regarding personal traits but, I would argue, also political views of the character. There needs to be no doubt in the mind of American audiences when it comes to films that deal with politics, that the protagonists are patriots.Stone’s film profits from this ambivalence in Snowden’s own political stance: at first he is more of a right winger who is a declared fan of Ayn Rand’s conservative-individualist manifesto Atlas Shrugged, then, after meeting his future partner Lindsey Mills, he turns slightly to the left, as he at one point states his support for President Obama. This also underlines the films ambiguity, as Oliver Stone openly stated about his Vietnam War film Platoon (1986) that “it could be embraced by … the right and the left. Essentially, most movies make their money in the middle” (Banff Centre). As Snowden takes the lie detector test as a part of the process of becoming a CIA agent, he confirms, quite sincerely it seems, that he thinks that the United States is the “greatest country in the world” and that the most important day in his life was 9/11. This again confirms his patriotic stance.Snowden is depicted as the exceptional individual, and at the same time the “ordinary guy”, who, through his act of courage, defied the all-powerful USA. During the aforementioned job interview scene, Snowden’s superior, Corbin O’Brian (Rhys Ifans), quotes Ayn Rand to him: “one man can stop the motor of the world”. Snowden states that he also believes that. The quote could serve as the film’s tagline, as a “universal truth” that seems to be at the core of American values and that also coincides with and reaffirms neoliberal ideology. Although it is undeniable that individuals can accomplish extraordinary feats, but when there is no systemic change, those can remain only solitary achievements that are only there to support the neoliberal “cult of the individual”.Snowden stands in total contrast to Assange in regard to his character and private life. There is nothing truly “problematic” about him, he seems to be an almost impeccable person, a “straight arrow”. This should make him a poster boy for American democracy and freedom of speech, and Stone tries to depict him in this way.Still, we are dealing with someone who cannot simply be redeemed as a patriot who did his duty. He cannot be unequivocally hailed as an all-American hero since betraying state secrets (and betrayal in general) is seen as a villainous act. For many Americans, and for the government, he will forever be remembered as a traitor. Greenwald writes that most of the people in the US, according to some surveys, still want to see Snowden in prison, even if they find that the surveillance by the NSA was wrong (365).Snowden remains an outcast and although the ending is not quite happy, since he must live in Russian exile, there is still a sense of an “upbeat final message” that ideologically colours the film’s ending.The Fifth EstateThe Fifth Estate is another example of the ideological view of the individual, but in this case with a twist. The film tries to be “objective” at first, showing the importance and impact of the newly established online platform WikiLeaks. However, towards the end of the film, it proceeds to dismantle Julian Assange (Benedict Cumberbatch) with the “everyone has secrets” platitude, which effectively means that none of us should ever try to reveal any secrets of those in power, since all of us must have our own secrets we do not want revealed. The film is shown from the perspective of Assange’s former disgruntled associate Daniel Domscheit-Berg (Daniel Brühl), who wrote a book about his time at WikiLeaks on which the film is partly based on (Inside WikiLeaks). We see Assange through his eyes and delve into personal moments that are supposed to reveal the “truth” about the individual behind the project. In a cynical twist, it is Daniel who is the actual whistleblower, who reveals the secrets of WikiLeaks and its founder.Assange, as it is said in the film, is denounced as a “messiah” or a “prophet”, almost a cult leader who only wants to satisfy his perverse need for other people’s secrets, except that he is literally alone and has no followers and, unlike real cult leaders, needs no followers. The point of whistleblowing is exactly in the fact that it is a radical move, it is a big step forward in ending a wrongdoing. To denounce the radical stance of WikiLeaks is to misunderstand and undermine the whole notion of whistleblowing as a part of true changes in a society.The cult aspects are often referred to in the film when Assange’s childhood is mentioned. His mother was supposed to be in a cult, called “The Family”, and we should regard this as an important (and bad) influence on his character. This notion of the “childhood trauma” seems to be a crutch that is supposed to serve as a characterisation, something the scriptwriting-guru Robert McKee criticises as a screenwriting cliché: “do not reduce characters to case studies (an episode of child abuse is the cliché in vogue at the moment), for in truth there are no definitive explanations for anyone’s behaviour” (376).Although the film does not exaggerate the childhood aspect, it is still a motive that is supposed to shed some light into the “mystery” that is Assange. And it also ties into the question of the colour of his hair as a way of dismantling his lies. In a flashback that resembles a twist ending of an M. Night Shyamalan thriller, it turns out that Assange actually dyes his hair white, witnessed in secret by Daniel, instead of it turning naturally white, as Assange explains on few occasions but stating different reasons for it. Here he seems like a true movie villain and resembles the character of the Joker from The Dark Knight (2008), who also tells different stories about the origin of his facial scars. This mystery surrounding his origin makes the villain even more dangerous and, what is most important, unpredictable.Žižek also draws a parallel between Assange and Joker of the same film, whom he sees as the “figure of truth”, as Batman and the police are using lies in order to “protect” the citizens: “the film’s take-home message is that lying is necessary to sustain public morale: only a lie can redeem us” (“Good Manners”). Rather than interpreting Assange’s role in a positive way, as Žižek does, the film truly establishes him as a villain.Fig. 2: The Problematic Individual: Julian Assange in The Fifth EstateThe Fifth Estate ends with another cheap psychologisation of Assange on Daniel’s part as he describes the “true purpose” of WikiLeaks: “only someone so obsessed with his own secrets could’ve come up with a way to reveal everyone else’s”. This faux-psychological argument paints the whole WikiLeaks endeavour as Assange’s ego-trip and makes of him an egomaniac whose secret perverted pleasure is to reveal the secrets of others.Why is this so? Why are Woodward and Bernstein in All the President’s Men depicted as heroes and Assange is not? The true underlying conflict here is between classic journalism; where journalists can publish their pieces and get the acclaim for publishing the “new Pentagon Papers”, once again ensuring the freedom of the press and “inter-systemic” critique. This way of working of the press, as the films show, always pays off. All the while, in reality, very little changes since, as Žižek writes, the “formal functioning of power” stays in place. He further states about WikiLeaks:The true targets here weren’t the dirty details and the individuals responsible for them; not those in power, in other words, so much as power itself, its structure. We shouldn’t forget that power comprises not only institutions and their rules, but also legitimate (‘normal’) ways of challenging it (an independent press, NGOs, etc.). (“Good Manners”)In the very end, the “real” journalism is being reinforced as the sole vehicle of criticism, while everything else is “extremism” and, again, can only stem from a frustrated, even “evil”, individual. If neoliberal individualism is the order of the day, then the thinking must also revolve around that notion and cannot transcend that horizon.ConclusionŽižek expresses the problem of revealing the truth in our day and age by referring to the famous fable “The Emperor’s New Clothes”, where a child is the only one who is naive and brave enough to state that the emperor is in fact naked. But for Žižek today,in our cynical era, such strategy no longer works, it has lost its disturbing power, since everyone now proclaims that the emperor is naked (that Western democracies are torturing terrorist suspects, that wars are fought for profit, etc., etc.), and yet nothing happens, nobody seems to mind, the system just goes on functioning as if the emperor were fully dressed. (Less than Nothing 92)The problem with the “Collateral Murder”, a video of the killing of Iraqi civilians by the US Army, leaked by Wikileaks and Chelsea Manning, that was presented to the public, for instance, was according to accounts in Inside Wikileaks and Inside Julian Assange’s War on Secrecy, that it did not have the desired impact. The public seems, in the end, to be indifferent to such reveals since it effectively cannot do anything about it. The return to the status quo after these reveals supports this stance, as Greenwald writes that after Snowden’s leaks there was no substantial change within the system; during the Obama administration, there was even an increase of criminal investigations of whistleblowers with an emergence of a “climate of fear” (Greenwald 368). Many whistleblower films assure us that in the end the system works; the good guys always win, the antagonists are punished, and laws have been passed. This is not to be accepted simply as a Hollywood convention, something that we also “already know”, but as an ideological stance, since these films are taken more seriously than films with similar messages but within other mainstream genres. Snowden shows that only individualism has the power to challenge the system, while The Fifth Estate draws the line that should not be crossed when it comes to privacy as a “universal” good because, again, “everyone has secrets”. Such representations of whistleblowing and disruption only further cement the notion that in our societies no real change is possible because it seems unnecessary. Whistleblowing as an act of revelation needs therefore to be understood as only one small step made by the individual that in the end depends on how society and the government decide to act upon it.References All the President’s Men. Dir. Alan J. Pakula. 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Method of Moments (MoM) is an integral equation based solver and is one of the most popular computational techniques to solve complex 3D Electromagnetic problems efficiently and accurately. Compared to the conventional differential equation solvers, MoM does not require a volumetric discretization of the entire bounding box containing the structure or imposes absorbing boundary condition or perfect match layer. However, due to Green's function interactions, the MoM matrix is dense leading to quadratic matrix fill time and cubic solve time complexity. As the scale and the complexity of the problem increases, matrix size increases with high storage memory and solve time requirement. Thus, to further expedite the solve time and decrease the storage requirement, fast solvers are extremely important. This thesis addresses the above problem by developing fast solvers and proposing a couple of novel preconditioning approaches for improving the solution speed of the fast solvers. The recent development of kernel-independent fast solvers has gained more popularity among the CEM community because of ease of their implementation. In this thesis, first, a brief overview of kernel dependent and kernel independent fast solvers is presented along with their parallelization. A new compression method is introduced based on the Adaptive Cross Approximation (ACA) sampling, where the pivot rows and columns can give a QR factorized orthogonal compressed matrices. These orthogonal matrices can be compressed further by using Interpolative Decomposition (ID) or can further be compressed by using Singular Value Decomposition (SVD) compression. The entire spectrum of fast solvers is highly dependent on the condition number of the matrices, specifically the spread of their eigenvalues. Hence, an ill-conditioned matrix jeopardizes the solution time and accuracy. This ill-conditioning mostly due to either geometry, meshing or the frequency of operation. Preconditioning the system of equations is the most efficient way to overcome ill-condition. Conventional preconditioners are either difficult to parallelize or lack linear scaling with problem size. In this thesis, we propose new preconditioners, which overcome the lacuna of the existing preconditioners. In the null-field preconditioner, near-field blocks are scaled to the diagonal blocks using the null-field method. The preconditioner is computed from all near-field blocks and selected far-field blocks in accordance with the null-field procedure. The final form of the preconditioner is block diagonal, therefore generates no additional fill-ins in its inverse and is also amenable to parallelization. A complexity analysis is presented to show the near-linear cost of preconditioner construction and usage in terms of computation time and memory. Numerical experiments with a sequential implementation demonstrate on an average 1.5-3x speed-up in the iterative solution time over Incomplete LU (ILUT) based preconditioners. Thus, giving a robust and stable preconditioner better than ILUT. The main drawback of the null-field method is the improper scaling of the near-field blocks. The next preconditioning method proposed in the thesis is based on the Schur’s complement method. The Schur’s complement method diagonalizes the near-field blocks to a block-diagonal form. The fill-in blocks generated in the process can be compressed efficiently and used for completely scaling the near-field blocks. Further fill-in reduction can be achieved by arranging the near-field blocks by using graph algorithms. Both these processes lead to a reduction in final matrix-vector product time in the iterative solver. Numerical experiments demonstrate a significant advantage over ILUT or recently published null-field based methods. In the case of multiport system or the problem with multiple Right Hand Side (RHS) iteration, the fast solver may turn out to be costly since each RHS may take different iteration thus taking more time to solve all RHSs so in such cases a direct solver is highly desirable. The complexity of the conventional direct solver is cubic so in this thesis, a fast direct solver based on the extended sparsification of FMM is proposed.